When a valve is closed suddenly in a pipe with flowing water, a water hammer pressure wave is set up. The very high pressures generated by such waves can damage the pipe. The maximum pressure, \(p_{\text {max }}\), generated by water hammer is a function of liquid density, \(ho\), initial flow speed, \(U_{0}\), and liquid bulk modulus, \(E_{v}\). How many dimensionless groups are needed to characterize water hammer? Determine the functional relationship among the variables in terms of the necessary \(\Pi\) groups.