1. The V-shaped tank has width w into the paper and is filled from the inlet pipe at volume flow Q. Derive expressions for (a) the rate of change dh/dt and (b) the time required for the surface to rise from h1 to h2.
2. A bellows may be modeled as a deforming wedge-shaped volume. The check valve on the left (pleated) end is closed during the stroke. If w is the bellows width into the paper, derive an expression for outlet mass flow m0 as a function of stroke θ(t).