Problem $1$

Total marks $[10]$

With the aid of a labelled diagram explain how the Energy Line and Hydraulic Grade line will change in simple

pipeline with pump and turbine. And draw the corresponding mechanical energy flow chart

Problem $2$

Total marks $[10]$

Water is pumped from a lower reservoir to a higher reservoir by a pump that provides $20$ kW of useful

mechanical power to the water. The free surface of the upper reservoir is $45$ m higher than the surface of

the lower reservoir. If the flow rate of water is measured to be $0\mathrm{.}03m\frac{3}{s},$ determine the irreversible head

loss of the system and the lost mechanical power during this process.

Problem $3$

Total marks $[10]$

Underground water is to be pumped by a $78$ percent efficient $5-kW$ submerged pump to a pool whose free

surface is $30-m$ above the underground water level. The diameter of the pipe is $7$ cm on the intake side

$($suction side$)$ and $5$ cm on the discharge side. Determine:

$($a$)$ The maximum flow rate of water

$($b$)$ The pressure difference across the pump inlet and the outlet

Problem $4$

Total marks $[10]$

With the aid of a labelled diagram, derive the equation for linear momentum equation that applies to fixed

control volume under steady state conditions.

Problem $5$

Total marks $[15]$

Water is flowing through a $10$ cm diameter water pipe at a rate of $0\mathrm{.}1\frac{m^3}{s}.$ Now a diffuser with an outlet

diameter of $20$ cm is bolted to the pipe in order to slow down water, as shown below.

a$)$ Disregarding frictional effects, determine the force exerted on the bolts due to the water flow.

b$)$ If the bolts are $2$ with $50$ mm in diameter, determine the stress in each bolt

Problem $6$

Total marks $[25]$

Water flows through a pipe bend and nozzle which lies with its axis in the horizontal plane. The water issues

from the nozzle into the atmosphere as a parallel jet with velocity of $16\frac{m}{s}$ and the gauge pressure at A is

$128k\frac{N}{m^2}.$ Neglecting friction, find the momentum of the resultant force due to the water$-$jet about a

vertical axis through point $x.$