Extra Momentum Transfer Questions
Content
A third year Chemical Engineering student is conducting experiments on laminar flow in a pipe using a liquid (incompressible). The pipe diameter is 6 mm and 1 m long. The student measures the flow rate through the pipe and the pressure drop and records the following observations: Flow rate (ml/min) Pressure drop (N/m2)
1.272 60.6
12.72 409
63.62 1016
127.2 1343
636.2 2191
1272 2616
6362 3952
(i)Is this fluid Newtonian or Non-Newtonian? (Justify your answer in not more than 5 sentences, marks will be awarded only if the justification is proper - 5 marks) (ii)If the fluid is Newtonian find viscosity, If the fluid is non-Newtonian calculate parameters for non-Newtonian rheology model (5 Marks) In a chemical plant, a 2 inch diameter pipe carries liquid at the rate of 1500 kg/hr (density = 850 kg/m 3, viscosity = 0.1 Pa-s) from equipment ‘A’ to ‘B’. The flow is controlled by a control valve (CV) at the desired rate. Equipment ‘A’ and ‘B’ are operated at a pressure of 2 barg and 0.5 barg respectively. Equipment ‘A’ is located on the ground floor, whereas equipment ‘B’ is located 15 m above ground level.The equivalent length of the pipeline excluding the control valve is 50m. Calculate the head loss coefficient of the control valve. If equipment ‘A’ is now operated at 3 barg pressure, what would be the new flow rate, assuming the equivalent length and head loss coefficient of the control valve to remain the same? B
CV A
The figure shows a part of a distillation column along with a condenser. It is desired to operate the distillation column at 5 mm Hg absolute pressure. This is done by using a vacuum pump and maintaining the condenser at 4 mm Hg absolute pressure. The vapor going from distillation column can be considered to be pure aniline (molecular weight = 93) at a temperature of 80 oC and a mass flow rate of 1000 kg/hr. At this temperature and pressure aniline can be considered to be an ideal gas. As an approximation, the variation of vapor density between the distillation column and the condenser can be neglected. The vapor viscosity can be considered to be 1x 10-5 Pas. The pipeline can be considered to have an equivalent length of 10 m. Estimate the diameter of the pipeline required.
5
A few days back, there was a newspaper report stating that a magnetic levitation (MAGLEV) train would travel at 500 km/hr. The cross sectional area of the train can be considered to be 5 m 2, and owing to the streamlined shape, the drag coefficient can be considered to be 0.5. (a) How much drag force would the train experience at this speed? (b) How much power would be required to overcome drag force at this speed?
In many chemical engineering operations fluids flow through a packed bed of particles. In one such operation water flows downwards (at a superficial velocity of 5 mm/s) through a 2 m diameter column containing a 10 m long packed bed of spherical particles (diameter = 100m, density = 1.4 g/cc, bed voidage = 0.7). (a)Estimate the pressure drop across the bed. (b)What pump power would be required in order to make the water flow through the bed? Q-1) A part of the equipment in a plant is shown on the right. At present, the two equipment 1 & 2 are placed vertically and connected by 6 inch pipeline. Water flows in the pipeline from ‘B’ to ‘A’ at the rate of 50 m3/hr. The height difference between the two points ‘A’ and ‘B’ is 8.3 metres. During a pressure survey in the plant, the pressure recorded at ‘B’ was found to be 1.89 barg, while that recorded at ‘A’ was found to be 0.34 barg. A “Smart” Second Year Chemical Engineering student suggest to the plant manager that the equipment be placed horizontally, in order to reduce the pressure difference between ‘A’ and ‘B’, as shown on the left. If all conditions remain the same, will pressure difference reduce? If so by how much? If not, why? A hovercraft ‘floats’ just above the surface of water or land. Its construction can be approximated as a platform floating just above the surface. Air is forced downwards through a central hole in the platform with the help of a ‘fan’ and escapes through the narrow opening between the platform and the surface. This is depicted in the Figure. Consider the weight of the platform and the people on the Hovercraft to be 5000 kg. Consider the gap between the platform and the surface to be 5mm. Consider the platform to be a square of 5m side. Consider air density to be 1.2 kg/m3. (A) In order to make the platform ‘float’ how much pressure would have to be generated below the platform? (B) Apply the Bernoulli equation between point ‘1’ below the platform and ‘2’ outside the platform. Velocity of air VO C O 2P / through the narrow gap and can be approximated by ‘orifice’ equation: , Value of CO can be taken as 0.6. Hence find velocity of the air through the 5 mm gap and the flow rate of air in m3/hr. (C)Now apply Bernoulli equation across the fan: neglect the losses, the change in velocity head and hydrostatic head across the fan. Calculate the power required by the fan for making the hovercraft float.
Car
A pump manufacturer gives the following relationship between dimensionless head number and dimensionless flow number for a certain type of pump impeller: N H = 12 – 2400 NQ2. It is desired to choose a pump that will deliver a flow of 90m 3/hr at a head of 60m, operating at a speed of 1440 rpm. The fluid may be assumed to be water. (a)What impeller diameter should be chosen? (b)Is the chosen pump operating at the ‘Best Efficiency Point’? Answer yes or no and justify your answer in not more than 5 sentences. A meteorological scientist is trying to predict the movement of rain drops in cumulous clouds. The scientist considers: (i) rain drop to be a sphere of 2 mm diameter, and (ii) the wind speed within the cloud to be 50 km/hr in the upward direction. Will the rain drop fall to the ground inspite of the upward air flow or will it be lifted to the top of the cloud by the air? Justify your answer with suitable calculations. What will be the velocity (magnitude and direction) of the drop with respect to ground? It is desired to fill 40 lit of petrol (density = 0.86 g/cc, viscosity = 0.5 centipoise, vapor pressure = 200mm Hg) in the car in 1 minute, from an underground storage tank. The level of petrol in the storage tank can be assumed to be 3.5m below the ground level, whereas the petrol tank of the car can be considered to be 1m above ground. The equivalent lengths of the pipe (1 inch in diameter) at
What is the available NPSH (in terms of water head)? Would 0.25 kW pump power be sufficient for this job, justify your answer with suitable calculations? A part of the cooling water pipeline in a plant is shown B The alongside. It transports cooling water from point ‘A’ to ‘B’. A diameter of the pipeline is 100mm ID and equivalent length between the points ‘A’ and ‘B’ is 150. It is desired to increase the flow rate of cooling water through the pipeline. In order to do this, one bright B. Chem. Engg. student suggests to the plant manager that another pipeline be put in and joined to pipeline AB at points ‘C’ and ‘D’ as shown alongside. The diameter of the C D B new pipeline is also 100 mm ID and has an equivalent length A of 50m. The equivalent length between ‘AC’ and ‘BD’ are also 50 m. Friction factorfor all pipes can be considered to be 0.01, and all the elevation differences can be neglected. The plant manager argues that since the line AB is unchanged, the flowrate through ‘AB’ is the bottleneck and hence the flow rate at B can not increase. You are expected to give your expert opinion on this dilemma. Assume that the pressures at ‘A’ and ‘B’ before and after the proposed modification remain the same. Does the flow rate of cooling water at ‘B’ increase or remains unaltered? If it changes then what is the % change in flow rate? The float of a rotameter is cylindrical in shape with 5 cm diameter and 5 height. The float is made of steel having density of 8 g/cc. The fluid is an liquid (density = 800 kg/m3, viscosity = 0.8 mPas). During an experiment, between the float and the wall of the rotameter tube is 5 mm at a liquid rate of 5 m3/hr. If the tube of the rotameter has an angle of divergence of calculate the change in height of the float when the flow rate is changed to m3/hr. A magnified picture (not to scale) is shown alongside to help you visualize the problem better.
cm organic the gap Float flow 5 mm 10o, 10 Flow 10o
Q-1)In an industry, a pipe of length ‘R’ cm is inclined at an angle of θ degrees. Fluid 1 is flowing in the pipe but the direction of the flow is not known. In order to determine the flow direction, a YOUNG CHEMICAL ENGINEER θ connects manometer between 1 and 2.After the manometer is connected and the flow starts and the pressure difference between ‘1’ and ‘2’ is measured with the help of a manometer. The height difference between the manometer limbs, when the flow occurs, is ‘R’ cm. Density of fluid 1 is (1000 – 10R) kg/m3 and R 1 that of fluid 2 is (2000+20R) kg/m3. Value of θ is as follows: Fluid If R < 25 then θ = 25. If 26<R<50 then θ = 50. If R > 51 then θ = 75. Answer: (1) If there was no flow and fluid 1 was stationary in the pipe, then pressure difference between ‘1’ and ‘2’ would be: P1 – P2 = _______________ N/m2 (2) As shown, under flowing conditions, the pressure difference:
R
R Fluid 2
P1 – P2 = ________________N/m2 (3) State whether the following statement is true of false:“The information given above and the answers to question (1) and (2) are enough to find out the flow direction” The above statement is TRUE / FALSE (circle your choice) (4) The flow direction “is from 1 to 2” / “is from 2 to 1” / “can not be determined” (strike out all those that are not applicable). Q-2) A petrol tank in a car is (30+R) cm deep. A pressure measurement device is connected to the bottom of the tank. The pressure measurement device measures gauge pressure (over and above atmospheric pressure) at the bottom of the tank and that is used to indicate the level of petrol in the tank. In one such case, during monsoon, accidently, water ingresses into the tank. Assume that the bottom ‘R/2’ cm of the tank is occupied by water. The gauge shows that the tank is (100 – R/2)% full of petrol. How much petrol is actually there as a percentage of the total capacity of the petrol tank.Assume that density of petrol is 0.7 g/cc. Ans: The petrol actually present is _____________% of the total tank capacity. Q-1) A part of the piping in a plant is shown alongside. The equivalent length of pipe between the two points ‘1’ and ‘2’ is ‘5R’ m. The vertical height difference between the two points is ‘30/R’ metres. The pipe diameter is ‘10+R/2’ mm. It is observed that the absolute pressure at point ‘1’ is ‘1000R’ N/m2 abs and absolute pressure at point ‘2’ is ‘10000/R’ mmHg abs. The density of the liquid is ‘1000+R’ kg/m3 and viscosity is ‘R’ centipoise. (1) The pressure difference between points 1 and 2, P1 – P2 is = ___________N/m2 (2) Therefore, the direction of flow is from point ‘_____’ to point ‘_____’. (3) The flow rate in the pipe is ________________ m3/hr (4) The Reynolds number is __________________ (5) The flow is in the laminar / turbulent regime (strike out whichever one is not applicable) (6) If you want to increase the flow rate in the pipe, without changing the heights (h1 and h2), the pressures P1 and P2, and the fluid; you will need to (fill in the blank with increase / decrease) ___________________ the value of ______________________. (7) In this pipe, the thickness of the laminar sub-layer is ________________ m A “CLOSED” tank containing water is connected to a 5 cm inner diameter Closed tank pipe as shown alongside. The total internal volume of the tank is 10m3. Initially the tank contains 5 m3 of water (remaining can be considered to be air at atmospheric pressure). The height difference between open end of the pipe and base of tank can be considered to be 2 m. The depth of water in the tank can be considered to be 2m. Initially the valve is closed and no water flows out from the open end of the pipe. This valve is now opened and water starts flowing out from the open end of the pipe and gradually water level in the tank starts depleting. When the valve is “open” the equivalent length of the pipe (from the tank to the open end of the pipe) can be considered to be 50m. For simplicity, the friction factor can be considered to be constant (irrespective of the Reynolds number) at 0.01. It is observed that water flow coming out
from the open end of the pipe reduces with time, and that, after some time, the water flow stops completely. Answer the following: (1) When the water flow stops, how much water (m3) would be left in the tank? (2) How much time would be required for 99% of this change to happen?
1.272 60.6
12.72 409
63.62 1016
127.2 1343
636.2 2191
1272 2616
6362 3952
(i)Is this fluid Newtonian or Non-Newtonian? (Justify your answer in not more than 5 sentences, marks will be awarded only if the justification is proper - 5 marks) (ii)If the fluid is Newtonian find viscosity, If the fluid is non-Newtonian calculate parameters for non-Newtonian rheology model (5 Marks) In a chemical plant, a 2 inch diameter pipe carries liquid at the rate of 1500 kg/hr (density = 850 kg/m 3, viscosity = 0.1 Pa-s) from equipment ‘A’ to ‘B’. The flow is controlled by a control valve (CV) at the desired rate. Equipment ‘A’ and ‘B’ are operated at a pressure of 2 barg and 0.5 barg respectively. Equipment ‘A’ is located on the ground floor, whereas equipment ‘B’ is located 15 m above ground level.The equivalent length of the pipeline excluding the control valve is 50m. Calculate the head loss coefficient of the control valve. If equipment ‘A’ is now operated at 3 barg pressure, what would be the new flow rate, assuming the equivalent length and head loss coefficient of the control valve to remain the same? B
CV A
The figure shows a part of a distillation column along with a condenser. It is desired to operate the distillation column at 5 mm Hg absolute pressure. This is done by using a vacuum pump and maintaining the condenser at 4 mm Hg absolute pressure. The vapor going from distillation column can be considered to be pure aniline (molecular weight = 93) at a temperature of 80 oC and a mass flow rate of 1000 kg/hr. At this temperature and pressure aniline can be considered to be an ideal gas. As an approximation, the variation of vapor density between the distillation column and the condenser can be neglected. The vapor viscosity can be considered to be 1x 10-5 Pas. The pipeline can be considered to have an equivalent length of 10 m. Estimate the diameter of the pipeline required.
5
A few days back, there was a newspaper report stating that a magnetic levitation (MAGLEV) train would travel at 500 km/hr. The cross sectional area of the train can be considered to be 5 m 2, and owing to the streamlined shape, the drag coefficient can be considered to be 0.5. (a) How much drag force would the train experience at this speed? (b) How much power would be required to overcome drag force at this speed?
In many chemical engineering operations fluids flow through a packed bed of particles. In one such operation water flows downwards (at a superficial velocity of 5 mm/s) through a 2 m diameter column containing a 10 m long packed bed of spherical particles (diameter = 100m, density = 1.4 g/cc, bed voidage = 0.7). (a)Estimate the pressure drop across the bed. (b)What pump power would be required in order to make the water flow through the bed? Q-1) A part of the equipment in a plant is shown on the right. At present, the two equipment 1 & 2 are placed vertically and connected by 6 inch pipeline. Water flows in the pipeline from ‘B’ to ‘A’ at the rate of 50 m3/hr. The height difference between the two points ‘A’ and ‘B’ is 8.3 metres. During a pressure survey in the plant, the pressure recorded at ‘B’ was found to be 1.89 barg, while that recorded at ‘A’ was found to be 0.34 barg. A “Smart” Second Year Chemical Engineering student suggest to the plant manager that the equipment be placed horizontally, in order to reduce the pressure difference between ‘A’ and ‘B’, as shown on the left. If all conditions remain the same, will pressure difference reduce? If so by how much? If not, why? A hovercraft ‘floats’ just above the surface of water or land. Its construction can be approximated as a platform floating just above the surface. Air is forced downwards through a central hole in the platform with the help of a ‘fan’ and escapes through the narrow opening between the platform and the surface. This is depicted in the Figure. Consider the weight of the platform and the people on the Hovercraft to be 5000 kg. Consider the gap between the platform and the surface to be 5mm. Consider the platform to be a square of 5m side. Consider air density to be 1.2 kg/m3. (A) In order to make the platform ‘float’ how much pressure would have to be generated below the platform? (B) Apply the Bernoulli equation between point ‘1’ below the platform and ‘2’ outside the platform. Velocity of air VO C O 2P / through the narrow gap and can be approximated by ‘orifice’ equation: , Value of CO can be taken as 0.6. Hence find velocity of the air through the 5 mm gap and the flow rate of air in m3/hr. (C)Now apply Bernoulli equation across the fan: neglect the losses, the change in velocity head and hydrostatic head across the fan. Calculate the power required by the fan for making the hovercraft float.
Car
A pump manufacturer gives the following relationship between dimensionless head number and dimensionless flow number for a certain type of pump impeller: N H = 12 – 2400 NQ2. It is desired to choose a pump that will deliver a flow of 90m 3/hr at a head of 60m, operating at a speed of 1440 rpm. The fluid may be assumed to be water. (a)What impeller diameter should be chosen? (b)Is the chosen pump operating at the ‘Best Efficiency Point’? Answer yes or no and justify your answer in not more than 5 sentences. A meteorological scientist is trying to predict the movement of rain drops in cumulous clouds. The scientist considers: (i) rain drop to be a sphere of 2 mm diameter, and (ii) the wind speed within the cloud to be 50 km/hr in the upward direction. Will the rain drop fall to the ground inspite of the upward air flow or will it be lifted to the top of the cloud by the air? Justify your answer with suitable calculations. What will be the velocity (magnitude and direction) of the drop with respect to ground? It is desired to fill 40 lit of petrol (density = 0.86 g/cc, viscosity = 0.5 centipoise, vapor pressure = 200mm Hg) in the car in 1 minute, from an underground storage tank. The level of petrol in the storage tank can be assumed to be 3.5m below the ground level, whereas the petrol tank of the car can be considered to be 1m above ground. The equivalent lengths of the pipe (1 inch in diameter) at
What is the available NPSH (in terms of water head)? Would 0.25 kW pump power be sufficient for this job, justify your answer with suitable calculations? A part of the cooling water pipeline in a plant is shown B The alongside. It transports cooling water from point ‘A’ to ‘B’. A diameter of the pipeline is 100mm ID and equivalent length between the points ‘A’ and ‘B’ is 150. It is desired to increase the flow rate of cooling water through the pipeline. In order to do this, one bright B. Chem. Engg. student suggests to the plant manager that another pipeline be put in and joined to pipeline AB at points ‘C’ and ‘D’ as shown alongside. The diameter of the C D B new pipeline is also 100 mm ID and has an equivalent length A of 50m. The equivalent length between ‘AC’ and ‘BD’ are also 50 m. Friction factorfor all pipes can be considered to be 0.01, and all the elevation differences can be neglected. The plant manager argues that since the line AB is unchanged, the flowrate through ‘AB’ is the bottleneck and hence the flow rate at B can not increase. You are expected to give your expert opinion on this dilemma. Assume that the pressures at ‘A’ and ‘B’ before and after the proposed modification remain the same. Does the flow rate of cooling water at ‘B’ increase or remains unaltered? If it changes then what is the % change in flow rate? The float of a rotameter is cylindrical in shape with 5 cm diameter and 5 height. The float is made of steel having density of 8 g/cc. The fluid is an liquid (density = 800 kg/m3, viscosity = 0.8 mPas). During an experiment, between the float and the wall of the rotameter tube is 5 mm at a liquid rate of 5 m3/hr. If the tube of the rotameter has an angle of divergence of calculate the change in height of the float when the flow rate is changed to m3/hr. A magnified picture (not to scale) is shown alongside to help you visualize the problem better.
cm organic the gap Float flow 5 mm 10o, 10 Flow 10o
Q-1)In an industry, a pipe of length ‘R’ cm is inclined at an angle of θ degrees. Fluid 1 is flowing in the pipe but the direction of the flow is not known. In order to determine the flow direction, a YOUNG CHEMICAL ENGINEER θ connects manometer between 1 and 2.After the manometer is connected and the flow starts and the pressure difference between ‘1’ and ‘2’ is measured with the help of a manometer. The height difference between the manometer limbs, when the flow occurs, is ‘R’ cm. Density of fluid 1 is (1000 – 10R) kg/m3 and R 1 that of fluid 2 is (2000+20R) kg/m3. Value of θ is as follows: Fluid If R < 25 then θ = 25. If 26<R<50 then θ = 50. If R > 51 then θ = 75. Answer: (1) If there was no flow and fluid 1 was stationary in the pipe, then pressure difference between ‘1’ and ‘2’ would be: P1 – P2 = _______________ N/m2 (2) As shown, under flowing conditions, the pressure difference:
R
R Fluid 2
P1 – P2 = ________________N/m2 (3) State whether the following statement is true of false:“The information given above and the answers to question (1) and (2) are enough to find out the flow direction” The above statement is TRUE / FALSE (circle your choice) (4) The flow direction “is from 1 to 2” / “is from 2 to 1” / “can not be determined” (strike out all those that are not applicable). Q-2) A petrol tank in a car is (30+R) cm deep. A pressure measurement device is connected to the bottom of the tank. The pressure measurement device measures gauge pressure (over and above atmospheric pressure) at the bottom of the tank and that is used to indicate the level of petrol in the tank. In one such case, during monsoon, accidently, water ingresses into the tank. Assume that the bottom ‘R/2’ cm of the tank is occupied by water. The gauge shows that the tank is (100 – R/2)% full of petrol. How much petrol is actually there as a percentage of the total capacity of the petrol tank.Assume that density of petrol is 0.7 g/cc. Ans: The petrol actually present is _____________% of the total tank capacity. Q-1) A part of the piping in a plant is shown alongside. The equivalent length of pipe between the two points ‘1’ and ‘2’ is ‘5R’ m. The vertical height difference between the two points is ‘30/R’ metres. The pipe diameter is ‘10+R/2’ mm. It is observed that the absolute pressure at point ‘1’ is ‘1000R’ N/m2 abs and absolute pressure at point ‘2’ is ‘10000/R’ mmHg abs. The density of the liquid is ‘1000+R’ kg/m3 and viscosity is ‘R’ centipoise. (1) The pressure difference between points 1 and 2, P1 – P2 is = ___________N/m2 (2) Therefore, the direction of flow is from point ‘_____’ to point ‘_____’. (3) The flow rate in the pipe is ________________ m3/hr (4) The Reynolds number is __________________ (5) The flow is in the laminar / turbulent regime (strike out whichever one is not applicable) (6) If you want to increase the flow rate in the pipe, without changing the heights (h1 and h2), the pressures P1 and P2, and the fluid; you will need to (fill in the blank with increase / decrease) ___________________ the value of ______________________. (7) In this pipe, the thickness of the laminar sub-layer is ________________ m A “CLOSED” tank containing water is connected to a 5 cm inner diameter Closed tank pipe as shown alongside. The total internal volume of the tank is 10m3. Initially the tank contains 5 m3 of water (remaining can be considered to be air at atmospheric pressure). The height difference between open end of the pipe and base of tank can be considered to be 2 m. The depth of water in the tank can be considered to be 2m. Initially the valve is closed and no water flows out from the open end of the pipe. This valve is now opened and water starts flowing out from the open end of the pipe and gradually water level in the tank starts depleting. When the valve is “open” the equivalent length of the pipe (from the tank to the open end of the pipe) can be considered to be 50m. For simplicity, the friction factor can be considered to be constant (irrespective of the Reynolds number) at 0.01. It is observed that water flow coming out
from the open end of the pipe reduces with time, and that, after some time, the water flow stops completely. Answer the following: (1) When the water flow stops, how much water (m3) would be left in the tank? (2) How much time would be required for 99% of this change to happen?
