### Fluid Mechanics - Problems

UNIT -I

1. A differential manometer is used to measure the pressure drop in a pipeline conveying methane gas at 20 oC and 1 atm pressure. The two liquids in the differential manometer are kerosene (specific gravity 0.82) and water. The inside diameter of the reservoirs and the U-tube manometer are 5cm and 0.5cm respectively. If the reading in the manometer is 15cm, calculate the pressure difference indicated, when the change in levels in the reservoir (i) is neglected and (ii) is taken into account.
2. A geometrically similar model of an air duct is built 1:30 scale and tested with water which is 50 times more viscous and 800 times more dense than air. When tested under dynamically similar conditions, the pressure drop is 2.25 atm in the model. Find the corresponding pressure drop in the full-scale prototype.
3. An inclined manometer is installed across a pipeline carrying water to measure the pressure drop due to friction. The manometer is filled with organic liquid of specific gravity 1.6 and its readings is 5 cm. The angle between the vertical and inclined limbs is 60o. Calculate the pressure drop.
4. A centrifuge bowl 30 cm in I.D. is rotating at a speed of 60 revolutions per second. It contains a 5 cm layer of a liquid of specific gravity 1.6. If the system is open to atmosphere, estimate the gauge pressure exerted at the walls of the centrifuge bowl.
5. Water at 20oC (viscosity = 1 cp) flows through a smooth straight pipe A of inside diameter 4 cm at an average velocity of 50 cm/sec. Oil flows through another pipe B of inside diameter 10 cm. Assuming similarities, calculate the velocity of oil through pipe B. Specific gravity of oil is 0.8 and its viscosity is 2 cp.
6. A U-tube manometer filled with mercury is connected between two points in a pipeline. If the manometer reading is 26 mm of Hg, calculate the pressure difference between the points when (a) water is flowing through the pipe (b) air at atmospheric pressure and 20oC is flowing in the pipe.

7. Density of mercury = 13.6 gm/cc Density of water = 1 gm/cc Molecular weight of air = 28.8

UNIT -II

8. Water flows through a 10-cm I. D. pipeline at an average velocity of 2m/s. Downstream the pipeline divides into a 10cm main and a 2.5 cm. bypass. The length of 10-cm. main pipeline in the bypassed section is 8 m. and the equivalent length of the bypass is 10 m. Neglecting entrance and exit losses, estimate the fraction of the total water flowing through the bypass, if the flow is turbulent.
9. Calculate the power required per meter width of the stream to force lubricating oil at a rate of 100 m3/hr per meter width through the space between two horizontal flat parallel plates. The plates are 3 m long and separated by a distance of 6 mm. The oil has a density of 0.9 gm/cc and a velocity of 25 cP. Make necessary assumptions.
10. Water is pumped from a reservoir to a height of 1000 m from the reservoir level, through a pipe of 15 cm I.D. at an average velocity of 4 m/s. If the pipeline along with the fittings is equivalent to 2000 m long and the overall efficiency is 70%, what is the energy required for pumping? Friction factor f = 0.046 Re-0.2.
11. Calculate the power required and the pressure which should be developed by a pump of efficiency 80% to pump 60 liters/ min. of 98% sulfuric acid at 25oC from an open tank at ground level to a closed overhead tank at a gauge pressure of 2 atm kept 3m above the ground. The density of the acid is 1850kg/m3 and the viscosity is 25 centipoises. Neglect frictional losses.
12. A horizontal annulus is 10 m long with an inner diameter of 2.5 cm and an outer diameter of 5.6 cm. A sugar solution of density 1300 kg/m3 and a viscosity of 60 cP is flowing through the annulus at 20oC. Calculate the volumetric flow rate when the impressed pressure drop is 40 kN/m2.
13. The pressures at two sections of a horizontal pipe are 0.3 kgf/cm2 and 0.6 kgf/cm2 and the diameters are 7.5 cm, and 15 cm respectively. Determine the direction of flow if water flows at a rate of 8.5 kg/sec. State your assumptions.
14. Water flows through a 0.203 m diameter pipe, with an average velocity of 3.6 m/sec. There is a sudden enlargement to 0.406 m diameter pipe. What is the power loss due to the sudden enlargement?
15. A capillary tube 0.2 cm in diameter and 10 cm long discharge one liter of a liquid in ten minutes under a pressure difference of 5 cm mercury. Find the viscosity of the liquid using the following data:
16. 2.16 m3/h water at 320 K is pumped through a 40 mm I.D. pipe through a length of 150 m in a horizontal direction and up through a vertical height of 12 m. In the pipe there are fittings equivalent to 260 pipe diameters. What power must be supplied to the pump if it is 60% efficient? Take the value of fanning friction factor as 0.008. Water viscosity is 0.65 cp, and density = 1 gm/cc.
17. A reaction vessel is provided with a bursting disc and the gases are vented to the atmosphere through a stack pipe having a cross sectional area of 0.07 m2. The rupture disc has a flow area of 4000 mm2 and the gases expand to the full area of the stack pipe in a divergent section. If the gas in the vessel is at a pressure of 10 MN/m2 and a temperature of 500 K. Calculate the initial rate of discharge of gas.
18. Water flows through a 100 mm steel pipe at an average velocity of 2 m/s. Downstream the pipe divides into a 100 mm main and a 25 mm bypass. The equivalent length of the bypass is 10 m; the length of the 100 mm pipe in the bypassed section is 8 m. Neglecting entrance and exit losses, calculate the fraction of the total water that passes through the bypass.

19. UNIT -III

20. Calculate the pressure drop of air flowing at 30oC and 1 atm pressure through a bed of 1.25 cm diameter spheres, at a rate of 60 kg/min. The bed is 125 cm diameter and 250 cm height. The porosity of the bed is 0.38. The viscosity of air is 0.0182 cP and the density is 0.001156 gm/cc.
21. If a spherical particle of 5 mm diameter and specific gravity 3.0 falls at a rate of 2 m/s through an oil of specific gravity 0.88, determine the viscosity of the oil.
22. A bed containing 32,700 kg of 100 mesh sharp sand is to be fluidized with air at 400oC and 17 atm abs in a cylindrical vessel 3.5 m in diameter. The ultimate density of the sand particle is 2690 kg/m3. The viscosity of air at operating conditions is 0.032 cp. Calculate

23. (a)the minimum height of fluidized bed
(b)the pressure drop across the bed at the minimum porosity condition
(c)the critical superficial air velocity, given minimum porosity = 0.55, diameter of 100 mesh particle size = 0.147 mm.

24. A mixture of vapors pass through a packed bed of glass spheres having density 2.4 g/cc each of diameter 0.5 cm. The pressure drop due to the flow is 405 kgf/m2. The height of packed bed is 1.85 m. The density and viscosity of the vapor mixture are 3.8 x 10-3 g/cc and 0.015 cP respectively.

25. Data:
Cross sectional area of the packed column tube = 0.09 m2
Bed porosity = 0.4
Find the mass flow rate of the vapor mixture. Is the bed fluidized?

26. A regenerative heater is packed with a bed of 6 mm cubes. The cubes are poured into the cylindrical shell of the regenerator to a depth of 3.5 m such that the bed porosity was 0.44. If air flows through this bed entering at 25oC and 7 atm abs and leaving at 200oC, calculate the pressure drop across the bed when the flow rate is 500 kg/hr per square meter of empty bed cross section. Assume average viscosity as 0.025 cP and density as 6.8 kg/m3.
27. A smooth flat plate is pulled through a pool of stagnant water at a velocity of 6 m/s. The plate has a width of 3 m and a length of 30 m. Estimate the total drag force acting on one side of the plate.
28. 7000 kg/hr of air, at a pressure of 7 atm and a temperature of 127oC is to be passed through a cylindrical tower packed with 2.5 cm Berl saddles. The height of the bed is 6 m. What minimum tower diameter is required, if the pressure drop through the bed is not to exceed 500 mm of mercury?

D p = (1.65 x 105 Z Vs1.82 r 1.85 )/Dp1.4
where
D p is the pressure drop in kgf/cm2, Z is the bed height in meter, r is the density in g/cc, Dp is nominal diameter of Berl saddles, Vs is the superficial linear velocity in m/sec.

UNIT -IV

30. A horizontal venturi meter having a throat diameter of 4 cm is set in a 10 cm I.D. pipeline. Water flows through the system and the pressure differential across the venturi meter is measured by means of a simple U-tube manometer filled with mercury. Estimate the flow rate when the manometer reading is 30 cm. Assume Cv = 0.98. If 10% of the pressure differential is permanently lost, calculate the power consumption of the meter.
31. The rate of flow of water in a 150 mm diameter pipe is measured with a venturi meter of 50 mm diameter throat. When the pressure drop over the converging section is 100 mm of water, the flow rate is 2.7 kg/sec. What is the coefficient of the meter?
32. Water is flowing through a 7.5 cm I.D. pipe. The corner taps of a 3 cm square edged orifice in the pipe are connected to a manometer containing methyl benzoate (sp.gravity = 1.10). the difference in liquid levels in the manometer is 30 cm. Find the flow rate.
33. Brine of specific gravity 1.2 is flowing through a 10 cm I.D. pipeline at a maximum flow rate of 1200 liters/min. A sharp edged orifice connected to a simple U-tube mercury manometer is to be installed for the purpose of measurements. The maximum reading of the manometer is limited to 40 cm. Assuming the orifice coefficient to be 0.62, calculate the size of the orifice required.
34. Water is flowing through a smooth pipe of 10 cm I.D. to which a horizontal venturi meter having a throat diameter of 4 cm is attached. A mercury U-tube manometer connected to the meter shows a reading of 25 cm. Calculate the flow rate.
35. A Newtonian fluid having a viscosity of 1.23 poise, and a density of 0.893 gm/cm3, is flowing through a straight, circular pipe having an inside diameter of 5 cm. A pitot tube is installed on the pipeline with its impact tube located at the center of the pipe cross section. At a certain flow rate, the pitot tube indicates a reading of 8 cm of mercury. Determine the volumetric flow rate of the fluid.
36. The rate of discharge of water from a tank is measured by means of a notch, for which the flow rate is directly proportional to the height of the liquid above the bottom of the notch. Calculate and plot the profile of the notch if the flow rate is 30 m3/hr, when the liquid level is 15 cm above the bottom of the notch.
37. A rotameter calibrated for metering has a scale ranging from 0.014 m3/min to 0.14 m3/min. It is intended to use this meter for metering a gas of density 1.3 kg/m3 with in a flow range of 0.28 m3/min to 2.8 m3/min. What should be the density of the new float if the original one has a density of 1900 kg/m3? Both the floats can be assumed to have the same volume and shape.

38. UNIT -V

39. A double acting reciprocating pump has a cylinder of 15 cm in diameter and an average stroke of 20 cm. The piston rod is 2.25 cm in diameter. The pump runs at a rate of 60 strokes per minute and discharges into a calibration tank of 1.2 m diameter. The pump discharges such that the water level in the tank rose by 1.30 m in a period of 2 minutes. Calculate the water-end efficiency of the pump.
40. A centrifugal pump is required to deliver 70 liters per second of water at room temperature against a head of 100 meters when running at 1450 rpm. Find the number of stages for best efficiency.
41. The impeller of a centrifugal pump has an external diameter of 45 cm and is 5 cm wide at the outer periphery. The impeller vanes are set at 35oC at this periphery. The impeller vanes are set at 35o at this periphery. The thickness of the vanes accounts for 7% of the flow area. The pump delivers at 200 liters/sec of water at 650 rpm against a manometric head of 12 meters. What is the manometric efficiency of the pump?
42. Crude oil is pumped at a rate of 80 liters/sec from a harbor to a refinery at a distance of 10 km through a 0.3 m I.D. pipeline. The crude oil has a density of 0.8 gm/cc and a viscosity of 5 cP. Calculate the power rating of the motor driving the pump, assuming an overall efficiency of 60% at full capacity.
43. Air is flowing in a smooth pipe having 1 m diameter at a rate of 340 m3/min. The length of the pipe is 250 m. The air temperature is 20 oC. What is the difference in elevation between the inlet and outlet if the static pressure change is zero? If a pump is to be installed keeping the pipe horizontal, which type of pump should be selected and what should be its theoretical power requirement? Assume that behaves an ideal gas.

44. Data:
Kinematic viscosity of air = 1.67 x 10-5 m2/sec.
Static pressure = 1 atm.

45. A petroleum fraction is pumped 2 km from a distillation plant to a storage tank through a mild steel pipeline 150 mm in diameter at the rate of 0.04 m3/sec. What is the pressure drop along the pipe and the power supplied to the pumping unit if it has an efficiency of 50%? The pump impeller is eroded and the pressure at its delivery falls to one half. By how much is the flow rate reduced? r = 0.705 g/cc m = 0.5 milli N.s/m2.