Solve any FOUR

1(a)
Define a fluid and explain Newton's law of viscosity

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1(b)
Explain boundary layer separation and methods to control it

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1(c)
A two dimensional flow is described in the Lagrangian system as

x = x

Find the equation of a fluid particlein the flow field

x = x

_{0}e^{-kt}+ y_{0}(1-e^{-2kt}) and y = y_{0}e^{-kt}.Find the equation of a fluid particlein the flow field

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1(d)
Explain Induced drag

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1(e)
Draw a sketch of an Orifice meter

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2(a)
Find the magnitude and direction of resultant pressure acting on a curved face of a dam which is shaped according to the relation y = x

^{2}/9 as shown in the figure. The height of the water retain by the dam is 10m. Consider the width of the dam as unity.

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2(b)
The stream lines is represented by Ψ = x

(i) Find its corresponding velocity potential

(ii) Determine the velocity and its direction at (2,2)

(iii) Sketch the streamlines and also show the direction of flow.

^{2}+y^{2}(i) Find its corresponding velocity potential

(ii) Determine the velocity and its direction at (2,2)

(iii) Sketch the streamlines and also show the direction of flow.

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3(a)
Starting from Navier stoke equation for incompressible laminar flow; derive an equation for velocity profile for Couette flow. State the assumptions made.

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3(b)
360 lit/sec of water is flowing in a pipe. The pipe is sent by 120°. The pipe bend measure 360 mm × 240 mm and volume at the bend is 0.14m

^{3}. The pressure at the entrance is 73 KN/m^{2}and exit is 2.4m above the entrance section. Find the resultant force and the direction on the bend
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4(a)
If velocity distribution, u in laminar boundary layer over a flat plate is assumed to be given by second order polynomial

u = a + by + cy

where y is the perpendicular distance measured from the surface of the flat plate, and a, b and c are constant. Determine the expression of velocity distribution in dimensionless form as, U is main stream velocity at boundary layer thickness δ. Further also find boundary layer thickness in terms of Reynolds number.

u = a + by + cy

^{2}where y is the perpendicular distance measured from the surface of the flat plate, and a, b and c are constant. Determine the expression of velocity distribution in dimensionless form as, U is main stream velocity at boundary layer thickness δ. Further also find boundary layer thickness in terms of Reynolds number.

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4(b)
A pipe 60 mm diameter and 450 m long slopes upwards at 1 in 50 an oil of viscosity 0.9 Ns / m

(1) Is the flow laminar?

(2) What pressure difference is required to attain this condition?

(3) What is the power of the pump required assuming overall efficiency 65%?

(4) What is the centre line velocity and the velocity gradient at pipe wall?

^{2}and sp. gr. 0.9 is required to be pumped at the rate of 5 liters/s(1) Is the flow laminar?

(2) What pressure difference is required to attain this condition?

(3) What is the power of the pump required assuming overall efficiency 65%?

(4) What is the centre line velocity and the velocity gradient at pipe wall?

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5(a)
Foe a normal shock wave in air Mach number is 3. If the atmospheric pressure and air density are 26.5 KN/m

^{2}and 0.413 kg/m^{3}respectively, determine the flow conditions before and after the shock wave. Tank γ = 1.4
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5(b)
Derive an expression of 'critical pressure ratio' for compressible fluid flow

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6(a)
A pipe pf diameter 0.4 m and of length 2000 m is connected to a reservoir at one end. The other end of the pipe is connected to a junction from which two pipes of length 1000m and diameter 30 cm runs parallel. These parallel pipes are connected to another reservoir which is having a level of water 10m below the water level of the above reservoir. Determine the total discharge, if coefficient of friction f=0.015.neglect the minor losses.

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6(b)
Explain

(i) Moodys Diagram

(ii) Major and Minor losses in pipes.

(i) Moodys Diagram

(ii) Major and Minor losses in pipes.

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