Solve any one question from Q1 and Q2

1 (a)
State and prove Pascal's law.

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1 (b)
Stream function is defined as:

ψ=x

Determine whether the flow is rotational or not. Also deduce the expression of velocity potential.

ψ=x

^{3}-3 xy^{2}:Determine whether the flow is rotational or not. Also deduce the expression of velocity potential.

6 M

2 (a)
A Newtonian liquid of kinematic viscosity 3 stokes flows over
a flat horizontal plate of surface area 0.8 m

^{2}. Velocity at y meters from plate is given as u = 2y - 2y^{3}in m/s. If shear force on plate is 0.352 N, find the density of liquid.
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2 (b)
Prove that streamlines and equipotential lines are orthogonal to each other.

6 M

Solve any one question from Q3 and Q4

3 (a)
Derive an expression for Bernoulli's equation along stream-line

6 M

3 (b)
A liquid of viscosity of 34.5 poise is flowing between two horizontal plates 50 mm apart with a maximum velocity of 2.5 m/s. Calculate:

(i) The discharge per meter width

(ii) Shear stress at the plates

(iii) The difference in pressure between two plates.

(i) The discharge per meter width

(ii) Shear stress at the plates

(iii) The difference in pressure between two plates.

6 M

4 (a)
Two orifices are placed in a vertical wall in such a way that lower one is 30 cm above the ground while upper one is
6 m above the first one. Horizontal distance travelled by the
jet from top orifice is 3 times than the one travelled by lower
jet. Both distances are measured at ground level. Assume
C

_{v}= 0.96 for both orifices, find the head of water behind the wall.
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4 (b)
Derive expression for velocity distribution for flow in fixed
parallel plates.

6 M

Solve any one question from Q5 and Q6

5 (a)
Derive an expression for Dupuit's equation.

6 M

5 (b)
Discharge Q of a centrifugal pump can be assumed to be dependent on density of liquid ρ viscosity of liquid μ, pressure p, impeller diameter D, and speed N in RPM. Using Buckingham π-theorem, show that: \[ Q=ND^3 \phi \left [ \dfrac {gH}{N^2 D^2}, \ \dfrac {v}{ND^2} \right ] \]

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6 (a)
Explain:

i) Reynolds number

ii) Weber number

iii) Euler number.

i) Reynolds number

ii) Weber number

iii) Euler number.

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6 (b)
Power is to be transmitted through 300 mm dia., 500 m long
pipe fitted with a nozzle at the end. The inlet is from a
reservoir where water level is 90 m above the nozzle. Calculate
the maximum power which can be transmitted and diameter
of nozzle required. Take f = 0.03.

7 M

Solve any one question from Q7 and Q8

7 (a)
Derive an expression for displacement, momentum and energy
Thicknesses.

9 M

7 (b)
A truck having a projected area of 6.5 m

^{2}, travelling 70 km/hr, has a total resistance of 2000 N. Of this 40% is due to rolling friction and 20% due to skin friction. The rest is due to pressure drag. Find the coefficient of pressure drag. Take ρ=1.22 kg/m^{3}for air.
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8 (a)
A metallic ball of diameter 0.04 m drops in a fluid of
specific gravity 0.7 and viscosity is 20 poise. Density of ball = 12000 kg/m

(i) Drag force exerted on ball

(ii) Pressure drag and friction drag

(iii) Terminal velocity of the ball.

^{3}. Determine:(i) Drag force exerted on ball

(ii) Pressure drag and friction drag

(iii) Terminal velocity of the ball.

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8 (b)
Write a short note on 'Separation of Boundary Layer its Control'.

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