Answer:
[tex]\frac{dV}{dt}= \frac{\pi d^2}{4}v[/tex]
Explanation:
The rate of volume flow out of tank can be expressed as:
[tex]\frac{dV}{dt} = A\frac{dL}{dt}[/tex]
where,
dV/dt = Volume flow rate
A = Cross-sectional area of outlet = πd²/4
d = diameter of circular outlet
dL = Displacement covered by water
dt = time taken
but we know that:
Velocity = Ï… = displacement/time = dL/dt
Substituting the values of "dL/dt" and "A" in the equation, we get:
[tex]\frac{dV}{dt} = \frac{\pi d^2}{4}v[/tex]
This is the expression for volume flow rate dV/dt, on terms pf v, d.
