# Mechanics of solids and fluids (1)

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1. An annular plate 4 m external diameter and 2 m internal diameter with its greatest and least depths below the surface being 3 m and 1.5 m respectively. Calculate the magnitude, direction and location of the force acting upon one side of the plate due to water pressure.

2. A pipe conveys 0.25 Kg/s of air at 300K and under an absolute pressure of 2.25 bar. Calculate the minimum diameter of pipe necessary if the flow velocity is limited to 7.5 m/s.

3. A 30 cm diameter pipe carries water under a head of 20 meters with a velocity of 3.5 m/s. If the axis of the pipe turns through 450 , find the magnitude and direction force on the bend.

4. A conical diffusing section diverges uniformly from 0.1 m diameter to 0.2 m diameter over a length of 1 metre. Find the local and convective acceleration at the middle of the diffuser. Consider the following two cases:

(i) rate of flow is 100 litres/sec at it remains constant,

(ii) rate of flow varies uniformly from 100 lit/sec to 200 litre/sec in 5 sec. and time of interest is when t = 2 sec.

Velocity at any cross section, perpendicular to the flow direction, may be assumed to be uniform.

5. A fire engine supplies water to a hose pipe 80 mm in diameter and 100 m long at a pressure of 300 KN/m 2 (gauge). The discharge end of the pipe has a nozzle fixed to it. For the momentum of issuing jet to be maximum, workout the nozzle diameter. Take friction factor 4f = 0.032 in the Darcy equation.

6. The velocity components in a 2 D incompressible flow field are expressed as:

u= (y^2 /3)+2x-(x^2) y; v=x(y^2) -2y- (x^2 /3)

Determine the velocity and acceleration at a point P ( x= 1m , y = 2 m)

Is the flow possible?