Question

A fire department’s tanker truck can hold 10 m3 of water (10,000 L, or about 2500 gallons). When in use, the truck forces water through a hose and out of a 3.0-cm-diameter nozzle with a speed of 8.50 m/s. (a) Use Bernoulli’s equation to find the absolute pressure inside the tank. Assume the speed of the water inside the tank is zero. (b) How long will it take to empty the tank at this rate? Assume the pressure inside the tank is kept constant. Give your answer in seconds and in minutes.

Answer 1

a)
P = pout + 0.5*rho*v^2
= 1*10^5 N/m^2 + 0.5*10^3*8.5
= 1*10^5 + 4250
=104250 N/m^2
Answer: 104250 N/m^2

b)
V = 10 m^3
A*v*t = V

v = 8.5 m/s

Area, A = pi*r^2
= pi*(1.5)^2
= 7.07 cm^2
= 7.07*10^-4 m^2

V = A*v*t
10 = (7.07*10^-4)*8.5*t
t = 166.4 s
= 2.77 min