Calculate the theoretical diameter of the pipe the nominal

Question

1. The diagram shown below represents a process for which a pump and associated pipe work require to be correctly sized.

The liquid is to be pumped from the underground storage vessel which is vented to atmosphere (assume 1 bar pressure) to a pressurised container supported some distance above ground level. The pump is sited at ground level and must be capable of delivering 0.01 m³s^-1 with a maximum velocity of 1.8 m s^-1.

Data:

Liquid density, ρ = 960 kg m^-3 Liquid viscosity, μ = 0.081 Pa s

(a) Calculate the theoretical diameter of the pipe; the nominal pipe diameter chosen from the table; and the actual average velocity in the nominal pipe.

Inside diameter (mm)
20
25
32
40
50
65
80
90
100

(b) Calculate Reynolds number for the process and hence the head loss due to friction. State any assumptions made.

(c) Using the following table for minor head losses, calculate the minor head losses for the system using both the equivalent length method and the number of velocity heads method. Compare the head losses estimated by each method.

Fitting	Equivalent length as number of pipe diameters	Number of velocity heads lost
Standard 90o bend	37	0.75
Entry to pipe	15	0.3
Exit from pipe	50	1

 

(d) Calculate the head required for the pump and its power requirement assuming a 70% efficiency.

(e) If the same pump was later used to pump water from the lower reservoir to the upper reservoir, what flow rate of liquid could be achieved? (N.B. This may require an iterative solution).

State any assumptions made.

Water density, ρ = 1000 kg m^-3

Water viscosity, μ = 0.001 Pas