The losses in the pipe increases the power requirement of the pipe to
maintain a given flowrate.
Responses (approximate value);
(a) 2.598 m/s
(b) 181,058.58
(c) 0.025
(d) 227:1000
(e) 1,216.67 W
<h3>Which methods can be used to calculate the pressure head in the pipe?</h3>The given parameters are;
Pump efficiency, η = 80%
Length of the pipe, L = 15 m
Cross-sectional diameter, d = 7 cm
Reservoir temperature, T = 20°C = 293.15 K
<em> </em>≈
≈ 1.0,
<em> </em> ≈ 0.4
Volumetric flow rate, Q = 10 Liters/s = 0.01 m³/s
Surface roughness, ∈ = 0.15 mm
(a) The cross sectional area of the pipe, A = π·r²
Where;
Which gives;
Therefore;
- The average velocity of the water, v ≈<u> 2.598 m/s</u>
(b) The viscosity of water at 20°C is 0.001003 kg/(m·s) given as follows;
Density of water at 20°C, ρ = 998.23 kg/m³
Reynolds' number, Re, is found as follows;
Which gives;
(c) The friction factor is given by the following formula;
Which gives;
- f ≈ <u>0.025</u>
(d) Friction head loss is given as follows;
Which gives;
Which gives;
Ratio between friction head loss and other head loss is therefore;
- The ratio between friction head loss and other head loss is approximately <u>227:1000</u>
(e) The power required <em>P</em> is found as follows;
Which gives;
- The power required to drive the pump, P ≈ <u>1,216.67 W</u>
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