$($ solve it for fluid mechanics$)$ A prototype gate valve which will control the flow in a pipe system conveying paraffin is to

be studied in a model. the pressure drop across the valve depend upon the gate opening h$,$ the

overall depth d$,$ the velocity V$,$ density rho and viscosity mu$.(15$ pts $)$

a$)$ please perform dimensional analysis to obtain the relevant non$-$dimensional group using the

gate opening $($h$)$; the velocity $($V$)$; and the viscosity $($mu$)$ as repeating variables

b$)$ For a particular opening, when the velocity of paraffin in the prototype is $3\mathrm{.}0$m$//$s what should

be the velocity of water in the model for the similarity$($The density and viscosity of paraffin

are $800$kg$//$m$^(3)$ and $0\mathrm{.}002$kg$//$m$*$s respectively. Take the kinematic viscosity of water as $).?$

c$)$ What will be the ratio of the quantities of flow in prototype and model?

d$)$ Find the pressure drop in the prototype if it is $60$ kPa in the model