Question 5.3: A process liquid is pumped from a storage tank to a distilla...

Static head

Difference in elevation, \Delta z=3.0-1.5=1.5 m

Difference in pressure, \Delta P=(1.7-1.013) 10^{5}=0.7 \times 10^{5} N / m ^{2}

as head of liquid =\left(0.7 \times 10^{5}\right) /(900 \times 9.8)=7.9 m

Total static ead =1.5+7.9=9.4 m

Dynamic head

As an initial value, take the fluid velocity as 1 m/s, a reasonable value.

Cross-sectional area of pipe =\frac{\pi}{4}\left(80 \times 10^{-3}\right)^{2}=5.03 \times 10^{-3} m ^{2}

Volumetric flow-rate =1 \times 5.03 \times 10^{-3} \times 3600=18.1 m ^{3} / h

Reynolds number r=\frac{900 \times 1 \times 80 \times 10^{-3}}{1.36 \times 10^{-3}}=5.3 \times 10^{4} (5.4)

Relative roughness = 0.46/80 = 0.0006

Friction factor from Figure 5.7,f = 0.0027

Length including miscellaneous loses =100+\left(600 \times 80 \times 10^{3}\right)=148 m

Pressure drop, \Delta P_{f}=8 \times 0.0027 \frac{(148)}{\left(80 \times 10^{-3}\right)} \times 900 \times \frac{1^{2}}{2}=\underline{\underline{17,982 ~ N / m ^{2}}} =17,982 /(900 \times 9.8)=\underline{\underline{2.03}} m \text { liquid } (5.3)

Total head = 9.4 + 2.03 = 11.4 m

To find the system curve the calculations were repeated for the velocities shown in the table below:

Plotting these values on the pump characteristic gives the operating point as 18.5 m at 40.0 m ^{3} / h and the pump efficiency as 79 per cent.