Solution

With:

density $=1000k\frac{g}{m^3}$

viscosity $=0,{804\mathrm{.}10}^{-3}N.\frac{s}{m^2}$

$g=10\frac{m}{s^2}$

Total pressure at junction A$-$B$-$C: $474,9\frac{J}{k}g$

Total pressure at junction C$-$D: $350,5\frac{j}{k}g$

Length section D: $99,5m$

Diameter section E: $4cm($slightly different solution is possible$)$

Pumping power: $11,7$kWGiven

Water is pumped from a $40-$meter high water tower into three different open reservoirs until the

water tower is empty. From these reservoirs, the water is sent through turbines for the generation of

electricity. The water in the tower is kept at a constant pressure of $5$ bar and a constant temperature

of $30C.$ The overall flow amounts to $120\frac{m^3}{h}.$ The piping system is given below. Some additional

characteristics are:

Section A: diameter $=10cm$

Section B: diameter $=6cm$; velocity $=8\frac{m}{s}$

Section C: diameter $=6cm$

Section D: diameter $=5cm$; velocity $=4\frac{m}{s}$

Section E: Reynolds number $=200\mathrm{.}000$

Wanted

a$)$ Determine the length of section $D.$

b$)$ Determine the diameter of section E$.$

c$)$ Determine the necessary pumping power.

Assumptions

Temperature changes in the pipes can be neglected.

All turns are sharp turns.

All tubes are smooth tubes.