Problem $3$:

The momentum equation for a control volume fixed in space is given by:

$\frac{d}{dt}{}_{V}VdV+{}_S(V*dS)V=-{}_S(p-p_{})dS+{}_{V}fdV+F_{\text{v}\text{i}\text{s}\text{c}\text{o}\text{u}\text{s}}$

Show how this equation would need to be modified if it were applied to each of the

following $($different$)$ scenarios:

a$)$ A control volume defined in a flow at steady state for which this no fluid is passing

the boundaries.

b$)$ A control volume defined in a flow at steady state for which gravitational forces and

pressure forces can be neglected.

c$)$ A control volume defined in a flow at steady state where the friction on a wall

boundary can be neglected.

d$)$ A control volume defined around a fluid in an open tank fitted with a pinhole at the

bottom from which fluid leaks out from over time.

e$)$ A control volume defined around a steady state flow that is only pressure driven.

For case e$)$: Express in $p_2$ in terms of all other variables, where D is a diameter