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VTU Civil Engineering (Semester 4)
Hydraulics & Hydraulic Machines
December 2014
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) The efficiency η of a fan depends on density ρ dynamic viscosity μ of the fluid, angular velocity ω, diameter D of the rotor and discharge Q. Express η as $\eta = f \left [ \dfrac {Q} {\omega D^3} , \ \dfrac {\mu} {\rho \omega D^2} \right ].$
8 M
1 (b) Derive different scale ratios as per Reynold's model law.
6 M
1 (c) A flow meter tested in the laboratory, gave a pressure drop of 200 kN/m2 for a discharge of 0.2m3/s in 200mm diameter pipe. If a geometrically similar model is tested in 1000mm diameter pipe at identical conditions of fluid, determine the corresponding discharge and pressure drop in the model.
6 M

2 (a) Distinguish between; Pipe flow and open channel flow.
6 M
2 (b) Derive the Chezy's equation for uniform flow in open channel with usual notations.
7 M
2 (c) A canal is to have a trapezoidal section with one side vertical and the other sloping at 60° to the horizontal. It has to carry water at 30m3/s with mean velocity 2 m/s. Compute the dimensions of the section which will require minimum lining.
7 M

3 (a) Define specific energy. Explain specific energy curve (sketch).
6 M
3 (b) A horizontal rectangular channel 4m wide carries a discharge of 16m3/s. If the initial depth of flow is 0.5m, determine is there a possibility of formation of hydraulic jump? If the jump forms, determine the sequent depth, Froude number after jump and energy loss.
6 M
3 (c) Give the classification of surface in case of GVF.
8 M

4 (a) Show that the efficiency of a jet striking a series of flat vanes mounted on the periphery of a circular wheel is maximum when the jet velocity is double of vane velocity and maximum efficiency is 50%.
10 M
4 (b) A jet of 30mm radius strikes normally on a fixed plate, with a velocity of 35m/s. Calculate the force exerted by the jet on the plate. If the plate is moving with 15 m/s in the direction of the plate, find the efficiency of the jet.
10 M

5 (a) Derive an equation of force exerted by a jet on an unsymmetrical curved vane tangentially, when vane K moving in the x-direction. Draw the velocity triangles and explain, also find the work done and efficiency.
10 M
5 (b) A jet of water with velocity 40m/s strikes a curved vane, which is moving with velocity 20m/s. The jet makes an angle of 30° with the direction of motion of vane at inlet and leaves at an angle of 90° to the direction of motion of vane at outlet. Draw the velocity triangles at inlet and outlet and determine the vane angles at inlet and outlet so that the water enters and leaves the vane without shock.
10 M

6 (a) Give the classification of turbine with examples.
10 M
6 (b) Design a Pelton wheel turbine required to develop 1471.5 kW power under a head of 160m at 420 rpm. The overall efficiency may be taken as 85%. Assume cv=0.98, co=0.46, jet ratio =12.
10 M

7 (a) Define draft tube. What are its functions?
6 M
7 (b) What is cavitation? How to eliminate it?
6 M
7 (c) A Kaplan turbine runner is to be designed to develop brake power of 7350 kW, under a head of 5.5 m. Diameter of bass of bass is 1/3rd of diameter of runner. Assuming speed ratio = 2.09, flow ratio=0.68, calculate; i) diameter of runner and boss; ii) speed of runner. Take η0=85%.
8 M

8 (a) Define:
i) Manometric efficiency
ii) Mechanical efficiency
iii) Overall efficiency
6 M
8 (b) Derive an expression for minimum starting speed of a centrifugal pump.
6 M
8 (c) The internal and external diameters of the impeller of a centrifugal pump are respectively 200mm and 40mm. The pump is running at 1200rpm. The vane angles of the impeller at inlet and outlet are 20° and 30°. Water enters radially and velocity of flow is constant. Determine the work done by the impeller per unit weight of water.
8 M

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