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Differential Question Help

The question states: "Fluid flows out of a cylindrical tank with a constant cross section. At time t, the volume of fluid remaining in the tank in V. The rate at which the fluid flows is proportional to the square root of V. Show that the depth h of the fluid in the tank satisfies the differential equation dh/dt = -k√h, where k is a positive constant"

What I did so far: dh/dt ∝-√V
so dh/dt=-k√V
What do I do now guys, you help is greatly appreciated! =)
Original post by Delta, Δ
The question states: "Fluid flows out of a cylindrical tank with a constant cross section. At time t, the volume of fluid remaining in the tank in V. The rate at which the fluid flows is proportional to the square root of V. Show that the depth h of the fluid in the tank satisfies the differential equation dh/dt = -k√h, where k is a positive constant"

What I did so far: dh/dt ∝-√V
so dh/dt=-k√V
What do I do now guys, you help is greatly appreciated! =)


Your first line should be dVdt\frac{dV}{dt} is proportional to V- \sqrt{V}


Posted from TSR Mobile
(edited 10 years ago)
Reply 2
Original post by LightBlueSoldier
Your first line should be dVdt\frac{dV}{dt} is proportional to V \sqrt{V}


Posted from TSR Mobile

Thanks for the reply. Why is it dV/dt that opposed to dh/dt? =)
Original post by Delta, Δ
Why is it dV/dt that opposed to dh/dt? =)


Because fluid is leaking at a rate proportional to the square root of V, so the volume is decreasing at that rate, not the height. The height is certainly decreasing, and we will have to set up an equation related to that, but from the information we have all we can directly say is that dV/dt is proportional to -V^1/2.
(edited 10 years ago)

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