Problem $4.$ A hydraulic accumulator is a device designed to reduce pressure pulsations in

hydraulic lines. It is essentially a pressure loaded cavity that can hold extra amounts of fluid.

Consider the accumulator below which services an injection system for lubricating oil $(=750$

$k\frac{g}{m^3}).$ The inlet radius is $R=0\mathrm{.}25m$ and the outlet is $R=0\mathrm{.}15m$

a$)(2$ pt$.)$ Redraw a simplified diagram of the accumulator and identify a control volume.

Show the influx and efflux vectors at the relevant control surfaces.

b$)(3$ pt$.)$ Initially, the system is at steady state with no accumulation. If the volumetric flow

rate at the exit is $Q=0\mathrm{.}59\frac{m^3}{s},$ what is the velocity at the outlet $(v_2)$ and the mass flow

rate?

c$)(5$ pt$.)$ The inlet velocity becomes equal to the outlet velocity. Explain why the system is

no longer at steady state. What is the mass accumulation rate if the velocity is $v=3\frac{m}{s}$

at both the inlet and outlet?