Compliance due to Entrapped Gas

the negative sign is used because the volume diminishes as the pressure increases. Assuming the process to be isothermal, the ideal gas law gives PV = Pg o- Thus, the compliance of the entrapped gas can be written as 

Let us assume that, pressure is everywhere at Pq for time t 0. At time t = 0, pressure is suddenly increased from Pq to Pq + AP. The liquid advances with a flow rate Q(t) and there is a change in the volume of gas given by 

Equation (2.111) is written using the incompressible property of the liquid. From chain rule, we get 

Let us consider another example of compliance, that is, a soft-walled channel. The channel is filled with incompressible liquid. The increase in pressure inside the channel leads to expansion 

We aiso assume that the pressure at the iniet be Pq at time t 0 and Pq + AP for time t 0. The flow rate equation between the iniet region and meeting point can be written as 

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