Question 11.1: Determine the loss of head in friction when water at 15 ºC f...
Determine the loss of head in friction when water at 15 ºC flows through a 300 m long galvanized steel pipe of 150 mm diameter at 0.05 m ^{3}/s. (kinematic viscosity of water at 15^{\circ} C =1.14 \times 10^{-6} m ^{2}/s. Average surface roughness for galvanized steel = 0.15 mm). Also calculate the pumping power required to maintain the above flow.
Average velocity of flow V=\frac{0.05}{(\pi / 4)(0.15)^{2}}=2.83 m/s
Therefore, Reynolds number Re =\frac{V D}{v}=\frac{2.83 \times 0.15_{1}}{1.14 \times 10^{-6}}=3.72 \times 10^{5}
Relative roughness \varepsilon / D=0.15 / 150=0.001
From Fig. 11.2, f = 0.02
Hence, using Eq. (11.6b)
h_{f}=\frac{\Delta p^{*}}{\rho g}=f \frac{L}{D}\left(V^{2} / 2 g\right) (11.6b)
h_{f}=0.02 \frac{300}{0.15} \frac{(2.83)^{2}}{2 \times 9.81}=16.33 m
Power required to maintain a flow at the rate of Q under a loss of head of h_{f} is given by
P=\rho g h_{f} Q
=10^{3} \times 9.81 \times 16.33 \times 0.05 W
= 8 kW
In the second and third categories of problems, both the flow rate and the pipe diameter are not known before hand to determine the friction factor. Therefore the problems in these categories cannot be solved by the straightforward application of Eq. (11.6b), as shown in Example 1 above. A method of iteration is suggested in this case where a guess is first made regarding the value of f. With the guess value of f the flow rate or the pipe diameter, whichever is unknown in the problem, is found out as a first approximation using the Eq. (11.6b). Then the guess value of f is updated with the new value of Reynolds number found from the approximate value of flow rate or pipe diameter as calculated. The problem is repeated till a legitimate convergence in f is achieved. Examples of this typical method dealing with the problems belonging to categories (ii) and (iii), as mentioned above, are given below:
