ME 2204 — FLUID MECHANICS AND MACHINERY
PART A — (10 × 2 = 20 marks)
1. Define – compressibility and bulk modulus.
2. Mention the significance of kinematic viscosity.
3. A circular and a square pipe are of equal sectional area. For the same flow rate, determine which section will lead to a higher value of Reynolds number.
4. What do you understand by hydraulic diameter?
5. Give the Rayleigh method to determine dimensionless groups.
6. Write down the dimensionless number for pressure.
7. A pump is to discharge 0.82 m3/s at a head of 42 m when running at 300 rpm. What type of pump will be required?
8. Mention the importance of Euler turbine equation.
9. Define slip in reciprocating machines.
10. Brief on acceleration head.
PART B — (5 × 16 = 80 marks)
11. (a) (i) A pipeline of 175 mm diameter branches into two pipes which delivers the water at atmospheric pressure. The diameter of the branch 1 which is at 35° counter-clockwise to the pipe axis is 75mm. and the velocity at outlet is 15 m/s. The branch 2 is at 15° with the pipe centre line in the clockwise direction has a diameter of 100 mm. The outlet velocity is 15 m/s. The pipes lie in a horizontal plane. Determine the magnitude and direction of the
forces on the pipes. (8)
(ii) Derive the linear momentum equation using the control volume approach and determine the force exerted by the fluid flowing through a pipe bend. (8)
(b) (i) A jet issuing at a velocity of 25 m/s is directed at 35° to the horizontal. Calculate the height cleared by the jet at 28 m from the discharge location? Also determine the maximum height the jet will clear and the corresponding horizontal location. (8)
(ii) Derive an expression for the variation of jet radius r with distance y downwards for a jet directed downwards. The initial radius is R and the head of fluid is H. (8)
12. (a) (i) Oil with a density of 900 kg/m3 and kinematic viscosity of 6.2 × 10–4 m2/s is being discharged by a 6 mm diameter, 40 m long horizontal pipe from a storage tank open to the atmosphere. The height of the liquid level above the center of the pipe is 3 m. Neglecting the minor losses, determine the flow rate of oil through the pipe. (8)
(ii) Two water reservoirs A and B are connected to each other through a 50 m long, 2.5 cm diameter cast iron pipe with a sharp-edged entrance. The pipe also involves a swing check valve and a fully open gate valve. The water level in both reservoirs is the same, but reservoir A is pressurised by compressed air while reservoir B is open to the atmosphere. If the initial flow rate through the pipe is 1.5 l/s, determine the absolute air pressure on top of reservoir A. Take the water temperature to be 25°C. (8)
(b) (i) In a water reservoir flow is through a circular hole of diameter D at the side wall at a vertical distance H from the free surface. The flow rate through an actual hole with a sharp-edged entrance (kL = 0.5) will be considerably less than the flow rate calculated assuming frictionless flow. Obtain a relation for the equivalent diameter of the sharp-edged hole for use in frictionless flow relations. (8)
(ii) A horizontal pipe has an abrupt expansion from 10 cm to 16 cm. The water velocity in the smaller section is 12 m/s, and the flow is turbulent. The pressure in the smaller section is 300 kPa. Determine the downstream pressure, and estimate the error that would have occurred if Bernoulli's equation had been used. (8)
(ii) The capillary rise h is found to be influenced by the tube diameter D, density ? , gravitational acceleration g and surface tension ? . Determine the dimensionless parameters for the correlation of experimental results. (6)
(b) (i) Using dimensional analysis, obtain a correlation for the frictional torque due to rotation of a disc in a viscous fluid. The parameters influencing the torque can be identified as the diameter, rotational speed, viscosity and density of the fluid. (8)
(ii) The drag force on a smooth sphere is found to be affected by the velocity of flow, u, the diameter D of the sphere and the fluid properties density ? and viscosity? . Find the dimensionless groups to correlate the parameters. (8)
14. (a) (i) A pump has to supply water which is at 70°C water at 90 m3/min and 1800 rpm. Find the type of pump needed, the power required, and the impeller diameter if the required pressure rise for one stage is 200 kPa; and 1250 kPa. (10)
(ii) A dam on a river is being sited for a hydraulic turbine. The flow rate is 1600 m3/h, the available head is 25 m, and the turbine speed is to be 460 rpm. Discuss the estimated turbine size and feasibility for a Francis turbine; and a Pelton wheel. (6)
(b) (i) A centrifugal pump with backward-curved blades has the following measured performance when tested with water at 20°C : Discharge Estimate the best efficiency point and the maximum efficiency. Also, estimate the most efficient flow rate, and the resulting head and brake power, if the diameter is doubled and the rotation speed
is increased by 50%. (10)
(ii) A Pelton turbine is to produce 18MW under a head of 450 m when running at 480 rpm. If D/d ratio is 10, determine the number of jets required. (6)
(ii) Discuss in detail about rotary positive displacement pumps. (8)
(b) (i) With a neat sketch explain the working of double acting reciprocating pump with its performance characteristics. (10)
(ii) In a single acting reciprocating pump the bore and stroke are 100 and 150 mm. respectively. The static head requirements are 4 m suction and 18 m delivery. If the pressure at the end of delivery is atmospheric calculate the operating speed. The diameter of the delivery pipe is 75 mm and the length of the delivery pipe is 24 m. Determine the acceleration head at ? =33 from the start of delivery. (6)