SELF EVALUATION EXERCISE $10\mathrm{.}1$

$1\mathrm{.}1$The following results were obtained during a laboratory test on a centrifugal pump:

$\backslash$table$[[$Discharge $($I$/$S$),0,38,61,76,98,121],[$Head $(m),37\mathrm{.}8,36\mathrm{.}3,33\mathrm{.}5,31\mathrm{.}7,27\mathrm{.}4,20\mathrm{.}1],[$Efficiency $(\%),0,54,64,68,70,67]]$

This pump is now used to pump water to a static height of $20m$ through a $150mm$ diameter pipe of effective length $83m.$ The friction factor $f$ is $0,0056.$ Plot the characteristic curves for the pump and determine

$($i$)$the discharge in $\frac{m^3}{s}$

$($ii$)$the operating head

$($iii$)$the power required to drive the pump.

$0,073\frac{m^3}{s}$;$32,2(m)$;$33,9(kW)$

$1\mathrm{.}2$After performing a laboratory test on a centrifugal pump the characteristic curve of the pump was found to obey the following equation:

$H=31,5+250Q-3600Q^2$

where $H$ is the effective $($manometric$)$ head in metres and $Q$ the discharge in $\frac{m^3}{s}.$

The pump is then used to deliver water through a pipeline $600m$ long, and $225mm$ in diameter, the static lift being $13,5m.$ The secondary losses due to bends and fittings amount to $20m$ equivalent pipe length. Take $f=0,008$ and determine:

$($a$)$ the delivery of the pump, in $\frac{m^3}{s}$

$($b$)$ the operating head of the pump

$($c$)$ the power required to drive the pump if the overall efficiency at this particular operating point is $67\%.$

$0,758\frac{m^3}{s}$;$29,8(m)$;$33,1(kW)$

CENTRIFUGAL PUMPS

$15$