Water is being pumped in the piping system shown below The p

Water is being pumped in the piping system shown below. The pump curve is approximated by the relation H_p = 150 - 5Q_1^2, with H_p in meters and Q_1 in m^3/s. The efficiency of the pump is 75%. Compute the flow distribution and find the required pump power.

Solution

The operating pressure of a pumped system is calculated in the SI unit of meters (m).

To maintain dimensional consistency, any pressure values used within the calculations are therefore converted from kPa into m using the following conversion

1 kPa = 0.102 m

the operating pressure or the total system head, HTotal , is defined as:

( ) HTotal = H s + H D + PRT - PRES … (1)

where, Hs = Static head (m)

HD = Dynamic head (m)

PRT = Pressure on the surface of the water in the receiving tank (m)

PRES = Pressure on the surface of the water in the reservoir (m)

Therefore, equation (1) becomes:

HTotal = H s + H D … (2)

. The dynamic head is calculated using the basic Darcy Weisbach equation given by:

HD 2 = K V SQUR / 2g … (3)

where K = loss coefficient

v = velocity in the pipe (m/sec)

g = acceleration due to gravity (m/sec 2 )

We can calculate the velocity in pipe using the following formula:

v = Q / A… (4)

where Q = flow rate through the pipe (m3 /sec)

A = pipe cross sectional area (CSA) (m2 )

The loss coefficient K is made up of two elements:

K = Kfittings + Kpipe … (5)

Kpipe is associated with the straight lengths of pipe used within the system and is defined as:

K pipe = Fl / D … (6)

where f = friction coefficient L = pipe length (m) D = pipe diameter (m)   

The power requirement for the pump can be calculated by:

P = (q * h * g * r) / pump efficiency

where P = Power (W)

r = Density (Kg/m 3 ) = 1000 kg/m 3 for water