Let V(t) be the volume of water in a tank (in liters), at time t (in seconds). W

Question

Let V(t) be the volume of water in a tank (in liters), at time t (in seconds). What are the meaning and units of dV/dt ? The tank is full at time t_o, so that V(t_0) > 0. At some later time ti a drain is opened 20 cm above the bottom of the tank (which is taller than 20 cm), emptying water from side of the tank. Is -- positive, negative or zero dt after the drain has been opened at , but before the water has dropped to 20 cm above the bottom of the tank? after the water drops to the drain hole 20 cm above the bottom of the tank? Let f(t) be the amount of rain in cm, that has fallen since midnight, with t measured in hours. Interpret the following in practical terms, giving units.

Explanation / Answer

1.

a] dV/dt means rate of change of volume w.r.t. time. its unit is meter cube per second or litres per second

b] if water is coming into the tank then dV/dt is positive, if water is flowing out of the tank then dV/dt is negative.

i. in this condition no water is flowing in or out of the tank hence dV/dt is zero.

ii. in this condition water is constantly flowing out of tank hence dV/dt is negative

iii. after falling upto the height od 20 cm again flow of the water stops hence dV/dt = 0

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