Derive the relation between the output the potential differe

Derive the relation between the output, the potential differences across the capacitor C of v_C, and the input v for the circuit shown in Figure Derive the relationship between the height h_2 and time for the hydraulic system shown in Figure Neglect inheritance.

Solution

Solution:

assumping a as area of connecting pipe

In tank1 heigh of water-level is h1

therefore velocity act at bottom is v= sqrt(2gh1)

discharge q2 is given av

q2 = a sqrt(2gh1) m3/s

this is the volume passing to second tank per second

total volume in tank2 is h2A m3

time t to reach this level = h2A/q2

t = h2A/(a sqrt(2gh1))