SPPU Mechanical Engineering (Semester 3)
Fluid Mechanics
May 2017
Total marks: --
Total time: --
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any one question from Q.1(a,b) &Q.2(a,b)
1(a) Explain:
i)Surface tension
ii) Compressibility
iii) Vapour pressure.
6 M
1(b) Explain stream function and velocity potential.
6 M

2(a) Define with mathermatical expression
i) Uniform and Non-uniform flow
ii) Steady and unsteady flows
iii) One, two and three dimensional flow.
6 M
2(b) A square plate 6m×6m is placed in a liquid of specific gravity 0.8 at an angle of 30° with free liquid surface A square hole of 1.5m×1.5m is cut exactly in centre of the palte. Its greatest and the least depths below free liquid surface are 5m and 2m respectively. Determine the total pressure on one face of the plate and position of centre of pressure.
6 M

Solve any one question from Q.3(a,b) &Q.4(a,b)
3(a) Derive Euler's equation for flow along streamline and deduce the Bernoulli's equation for the same.
6 M
3(b) A 0.2m diametere pipe carries liquid in laminar region. A Pitot tube placed in the flow at a radial distance of 15mm from the axis of the pipe indicates velocity of 0.5 m/s. Calculate:
i) The maximum velocity
ii) The mean velocity
iii) The discharge in the pipe.
6 M

4(a) Derive an expression of velocity and shear stress distribution for laminar flow between fixed parallel plates.
6 M
4(b) The inlet and thorat diameters of horiziontal venturimeter are 30 cm and 10 cm respectively. The liquid flowing through the meter is water. The pressure intensity in inlet 13.734 kN/m2 while vacuum pressure heat at the throat is 37 cm of mercury. Find the rate of flow. Assume that 4% of the differential heads is lost between the inlet and outlet. Find also the value Cd for venturimeter.
6 M

Solve any one question from Q.5(a,b) &Q.6(a,b)
5(a) A 2500 m long pipeline is used for transmission of poower. 120kW power is to be transmitted through the pipe in which wate having a pressure of 4000 kN/m2 at inlet is flowing. If the pressure drop over the length of pipe is 800kN/m2 and f = 0.024, find:
i) Diameter of the pipe
ii) Efficiency of transmission
7 M
5(b) Explain:
i) Mach Number
ii) Froude Number
iii) Eulet Number.
6 M

6(a) Discharge Q of a centrifugal pump can be assumed to be dependent of density of liquid ρ, viscosity of liquid μ , pressure, impeller diameter D, and speed N in RPM. Using Buckingham π theorem, show that:\[Q=ND^{3}\phi \left [ \frac{gH}{N^{2}D^{2},\frac{v}{ND^{2}}} \right ]\]
7 M
6(b) Derive an expression for Darcy-Weisbach equation.
6 M

Solve any one question from Q.7(a,b) &Q.8(a,b)
7(a) Write a short note on " Boundary layer formation over flat plate.
7 M
7(b) A cylinder 80mm diameter and 200 long is placed in a stream of fluid flowing at 0.5 m/s. The axis of the cylinder is normal to the direction of flow. The density of fluid in 800 kg/m3. The drag force is measure and found to be 30 N. Calculate the drag coefficient. At a point on the surface the pressure is measured as 96 Pa above the ambient level. Calculate the velocity at this point.
6 M

8(a) Derive an expression for displacement, momentum and energy thicknesses.
9 M
8(b) What is Drag and Lift? Explain different types of drag on an immersed body.
4 M

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