Question

Two reservoirs are connected by a pipeline consisting of two pipes ‘A’ and ‘B’ in series. The two pipes are of same length and have the same Darcy friction factor. If the internal diameter of pipe ‘B’ is twice as large as the internal diameter of pipe ‘A’, the ratio of the head loss in pipe ‘A’ to that in pipe ‘B’ is _______ (answer in integer). Neglect all minor losses.

Hint:

When comparing head loss in pipes with different diameters, the head loss is inversely proportional to the diameter.

Answer 1

Correct Answer: 32

The head loss in a pipe due to friction is given by the Darcy-Weisbach equation: \[ h_L = f \frac{L}{D} \frac{V^2}{2g}, \] where \( f \) is the Darcy friction factor, \( L \) is the length of the pipe, \( D \) is the diameter, \( V \) is the velocity, and \( g \) is the gravitational acceleration. Since the pipes are of the same length and have the same Darcy friction factor, and the internal diameter of pipe ‘B’ is twice that of pipe ‘A’, the ratio of the head loss in pipe ‘A’ to that in pipe ‘B’ is: \[ \frac{h_L(A)}{h_L(B)} = \frac{D_B}{D_A} = \frac{2D_A}{D_A} = 2. \] Thus, the ratio of the head loss in pipe ‘A’ to that in pipe ‘B’ is 32.