a$)$ Describe the Loop or 'Head Balance' method solution procedure.

b$)$ Figure $5\mathrm{.}1$ below shows concrete flows into a cart sitting on a scale. The

stream of concrete has a density of $68k\frac{g}{m^3},$ an area of $0\mathrm{.}092m^2,$ and a

speed of $4\frac{m}{sec}.$ At the instant shown, the weight of the cart plus the

concrete is $3560N.$ Determine the tension in the cable and the weight

recorded by the scale. Assume steady flow.

c$)$ Three large reservoirs are joined by a branching pipeline exactly as shown

in Figure $5\mathrm{.}2$ below. The elevation of the water surface in the reservoirs is

$A=680m$;$C=640m$; and $D=590m.$ These levels do not change. Pipe

details are as follows:

Head loss in metres is given by the formula: $h=K{Q}^2$ where $Q$ is the

discharge in $\frac{m^3}{s},K$ is a coefficient combining pipe length diameter and

friction factor.

Estimate the discharges in each pipe and the head at junction B neglecting

all head losses except those due to friction.

Figure $5\mathrm{.}2$