Question

A water pipe tapers down from an initial radius of R₁ = 0.2 m to a final radius of R₂ = 0.09 m. The water flows at a velocity v₁ = 0.86 m/s in the larger section of pipe.

1. Using this water supply, how long would it take to fill up a swimming pool with a volume of V = 130 m³? (give your answer in minutes)
2. The water pressure in the center of the larger section of the pipe is P₁ = 243120 Pa. Assume the density of water is 10³ kg/m³. What is the pressure in the center of the smaller section of the pipe?
3.

Answer 1

Volumetric flow of water = v1 * a1
V = 0.86 * π * 0.2^2 m^3/s
V = 0.108 m^3/s

Time it would take to fill the swimming pool, = 130 / 0.108 s
t = 1203.7 s
Converting to minutes,
t = 20.1 min


(2)
P1 = 243120 Pa
p = 10^3 kg/m^3

Using eq of continuity,
a1 * v1 = a2 * v2
π*r1^2 * v1 = π*r2^2 * v2
v2 = 0.86 * (0.2^2/0.09^2)
v2 = 4.25 m/s

Using Bernoulli's theorem,
P1 + 1/2*p*v1^2 = P2+ 1/2*p*v2^2
243120 + 1/2 * 1000 * 0.86^2 = P2 + 1/2 * 1000 * 4.25^2
P2 = 234459 Pa
pressure in the center of the smaller section of the pipe, P2 = 234459 Pa