Question $3(25\%)$

Water flows from a large reservoir A through pipes to tank $B.$ The system operates at a flow rate

$Q=0\mathrm{.}1\frac{m^3}{s}.$ The pipes are made of commercial steel with a diameter of $d=150mm($see

Figure $3).$ The density and viscosity of the water are $=1000\frac{kg}{m^3}$ and

$u=1\mathrm{.}13{10}^{-6}\frac{m^2}{s},$

respectively.

The pressure in tank $B$ is given as $p_2=40$kPa.

a$.$ What should the pressure $p_1$ be above reservoir $A$ to maintain the flow? $(10$ points$)$

b$.$ What is the horizontal force $($magnitude and direction$)$ acting on the upper bend of the pipe?

Assume that internal friction in the bend is negligible and that the velocity is fully developed at the

outlet of the bend. $(10$ points$)$

c$.$ Instead of maintaining the pressure in tank $A,$ it has been proposed to use a pump characterized

by the curve in Figure $4$ to maintain the flow to tank $B.$ Is it possible to operate the pump for this

task? Justify your answer and show the steps. Use a friction factor $f=0\mathrm{.}016.(5$ points$)$

Figure $3$: Water flow system from reservoir $A$ to tank $B.$

Figure $4$: Pump characteristic curve for part c$.$