Math Problem from Cambridge Olevel Past paper

Question

How long did 9600cm3 of water take to enter to a tank through a pipe of radius 0.8cm if it flowed at a rate of 25cm per second?

Answer 1

first you want to compute the area of the pipe's opening by taking

A = pi*r^2

A = pi(0.8)^2

A = 2.01 cm^2

then you can calculate the volumetric flow rate of the water by taking

Flow Rate = Area x Speed

Flow Rate = 2.01 cm^2 * 25 cm/s

Flow Rate = 50.27 cm^3/s

finally then you can find the time it takes to fill the tank by taking

Time = Total Volume / Flow Rate

Time = 9600 cm^3 / (50.27 cm^3/s)

Time = 190.99 seconds

so it would take approximately 191 seconds for the water to enter the tank

Answer 2

If the linear flow velocity is 25 cm/s, and the pipe radius is 0.8 cm², then the volume transfer rate per time is the area of the pipe times the velocity. That is, π*0.8²*25 cm³/s = 50.26 cm³/s. The time it takes this to fill a volume of 9600 cubic centimeters is thus 9600/50.26 s ≈ 192 s.