Question

Water is moving with a speed of 5.5 m/s through a pipe with a cross-sectional area of 4.6 cm2. The water gradually descends 11 m as the pipe increases to 9.0 cm2. (a) What is the speed at the lower level? (b) If the pressure at the upper level is 1.7 × 105 Pa, what is the pressure at the lower level?

Answer 1

here,

the speed at upper level , v1 = 5.5 m/s

the cross-sectional area , A1 = 4.6 cm^2

A1 = 4.6 * 10^-4 m^2

h = 11 m

the cross-sectional area at lower level , A2 = 9 cm^2 = 9 * 10^-4 m^2

a)

let the speed at the lower level be v2

using equation of continuity

A1 * v1 = A2 * v2

4.6 * 10^-4 * 5.5 = 9 * 10^-4 * v2

v2 = 2.81 m/s

the speed at the lower level is 2.81 m/s

b)

the pressure at upper level , P1 = 1.7 * 10^5 Pa

let the pressure at the lower level be P2

using Bernauli's theorm

P1 + p * g * h + 0.5 * p * v1^2 = P2 + 0.5 * p * v2^2

1.7 * 10^5 + 1000 * 9.81 * 11 + 0.5 * 1000 * 5.5^2 = P2 + 0.5 * 1000 * 2.81^2

solving for P2

P2 = 2.89 * 10^5 Pa

the pressure at the lower level is 2.89 * 10^5 Pa