The figure shows an accumulator similar to the one in Figure 4.26. In this case, there is a distinction between the fluid pressure P 3 and the pressure of the gas in the rubber bladder under some...

The figure shows an accumulator similar to the one in Figure 4.26. In this case, there is a distinction between the fluid pressure P₃
and the pressure of the gas in the rubber bladder under some conditions. Before the fluid system is pressurized, when P₃
is zero, the pressure in the gas is P₀
and the volume of the gas is V₀. The bladder has a rigid section at the base that prevents it from expanding into the inlet pipe. Until the fluid pressure exceeds P₀, no fluid enters the accumulator; Q₃
= 0. However, after some fluid has entered the accumulator, the gas is compressed and the gas pressure and the fluid pressure are essentially identical.

Consider the volume of fluid that has entered the accumulator, V₃
=
 dt, to be zero at t = 0 when the system is unpressurized. Make a sketch of the nonlinear capacitance relationship between P3 and V 3 using the isentropic assumption discussed in the text. Note that the P₃
can rise to P₀
even when V₀
= 0 and that P₃
→ ∞ when V₃
→ V₀.