The bulk modulus (\( K \)) is calculated using:
\( K = \frac{\Delta P}{\Delta V / V} \)
Substituting \( \Delta P = 500 \, \text{kPa}, \, V = 2 \, \text{m}^3, \) and \( \Delta V = 0.004 \, \text{m}^3 \), we find:
\( K = \frac{500}{0.004 / 2} = 25 \, \text{MPa}. \)
The shaft of a 6 m wide gate in the figure will fail at a moment of 3924 kN.m about the hinge P. The maximum value of water depth \( h \) (in m) that the gate can hold is ......... (round off to the nearest integer).
Consider steady flow of water in the series pipe system shown below, with specified discharge. The diameters of Pipes A and B are 2 m and 1 m, respectively. The lengths of pipes A and B are 100 m and 200 m, respectively. Assume the Darcy-Weisbach friction coefficient, \( f \), as 0.01 for both the pipes.
The ratio of head loss in Pipe-B to the head loss in Pipe-A is ___________ (round off to the nearest integer).