A hot water tank is to be filled with water by the technicia

A hot water tank is to be filled with water by the technician that has a volume of V with units of m^3. He plans to use a hose nearby which has a diameter of D, in m. The average velocity of the water leaving the hose is v, having units of m/s. Obtain a relation to determine the amount of time (t) in seconds (s) it will take to fill the tank.

Solution

Given that,

Volume of the tank is V in m^3.

Diameter of the hose is D in m

Average Velocity is v in m/sec

time is t in sec.

We know

Cross section of circular hose A= (/4)*D²

volume flow rate/Discharge per second Q= Av

                                           =(/4)*D²*v

Time taken to fill the tank= V/Q

But we have Q=(/4)*D²*v

therefore

Amount of Time required=(V)/(/4)*D²*v

                                       t =4V/(D²*v) sec