# Question No.1

#### Topic : Pump-Pipeline System Analysis & Design

Tests on a physical model pump indicated a cavitation number of 0.12. A homologous (geometrically and dynamically similar) unit is to be installed where the atmospheric pressure is 950 mb, and the vapour pressure head 0.2 m. The pump will be situated above the suction well, the suction pipe being 200 mm in diameter, of uPVC, 10 m long; it is vertical with a 90o elbow leading into the pump inlet and is fitted with a foot valve. The foot valve head loss hv = 4.5 vs2 / 2g; bend loss hb = 1.0 vs2 / 2g. The total head at the operating discharge of 35 lit/sec is 25 m. Calculate the maximum permissible suction head and suction lift.

Given :

• $σ=0.12$
• $hv=4.5vs22g$
• $hb=1.0vs22g$

Steps of solution :

Convert atmospheric pressure value in head of water :

Calculate the required net positive suction head :

$σ=NPSHRHm$ $→$ $0.12=NPSHR25$ $→$

The maximum permissible suction head :

The friction losses occurring in the suction pipe :

$vs=QoAs=Qoπ4Ds2$ $→$

To calculate Reynolds number :

$Re=vDν=1.114∗0.21.004∗10−6=221,929$

The roughness height for uPVC pipes is :

To calculate the friction coefficient, Barr's equation is used :

$1f=−2logk/D3.7+5.1286Re0.89$

$1f=−2log0.03/0.23.7+5.1286221,9290.89$ $→$ $fs=0.0166$

To calculate K for the suction pipe (using Darcy-Weisbach equation) :

$K=8fLπ2gD5$ $→$ $K=8fsLsπ2gDs5$

$K=8∗0.0166∗10π2∗9.81∗0.25=42.749$

To calculate the friction losses through the suction pipe :

To calculate the minor/secondary losses through the suction pipe :

$hminor=hv+hb$

To calculate the total head losses occurring through the suction pipe :

To calculate the suction lift :