a) Derive Bemoulli's equation and hence deduce an expression that gives the discharge measured by a venturimeter from first principles. b) A Venturimeter is to fitted in a horizontal pipe of \( \mathbf{0 . 1 5} \mathbf{~} \mathbf{m} \) diameter to measure a flow of water which may be anything up to \( 240 \mathrm{~m}^{3} / \) hour. The pressure head at the inlet for this flow is \( \mathbf{1 8} \mathbf{~ m} \) above atmospheric and the pressure head at the throat must not be lower than \( 7 \mathrm{~m} \) below atmospheric. Between the inlet and the throat there is an estimated frictional loss of \( 10 \% \) of the difference in pressure head between these points. Calculate the minimum allowable diameter for the throat. [10]