Water at $25^{\circ}$ C is flowing through a 1.0 km long G.I. pipe of 200 mm diameter at the rate of $0.07 m^{3} / s$ . If value of Darcy friction factor for this pipe is 0.02 and density of water is $1000 k g / m^{3}$ , the pumping power (in kW) required to maintain the flow is

1.8

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17.4

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20.5

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41.0

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Solution

The correct option is B 17.4
Given data:
Length; L = 1 km = 1000 m
Diameter; d = 200 mm = 0.2 m
Discharge; Q = 0.07 $m^{3} / s$

Friction factor,
f = 0.02
Density; $ρ = 1000 k g / m^{3}$

$Q = A V = \frac{π}{4} d^{2} V$

$0.07 = \frac{3.14}{4} \times (0.2)^{2} \times V$

or V = 2.23 m/s

We know that head loss due to friction,

$h_{1} = \frac{f L V^{2}}{2 g d} = \frac{0.02 \times 1000 \times (2.23)^{2}}{2 \times 9.81 \times 0.2}$

= 25.34 m

Pumping power required to maintain the flow,
$P = ρ Q g h_{1}$
$= 1000 \times 0.07 \times 9.81 \times 25.34$
$= 17400.9 W = 17.4 K W$

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Water at 25∘C is flowing through a 1.0 km long G.I. pipe of 200 mm diameter at the rate of 0.07 m3/s. If value of Darcy friction factor for this pipe is 0.02 and density of water is 1000 kg/m3, the pumping power (in kW) required to maintain the flow is

Water at $25^{\circ}$ C is flowing through a 1.0 km long G.I. pipe of 200 mm diameter at the rate of $0.07 m^{3} / s$ . If value of Darcy friction factor for this pipe is 0.02 and density of water is $1000 k g / m^{3}$ , the pumping power (in kW) required to maintain the flow is