Question

Water is flowing in a straight horizontal pipe of variable cross section. Where the cross-sectional area of the pipe is 2.90·10-2 m2, the pressure is 10.90·105 Pa and the velocity is 0.310 m/s. In a constricted region where the area is 10.30·10-4 m2, what is the velocity? (in m/s)

A: 1.97 B: 2.86 C: 4.15 D: 6.02 E: 8.73 F: 1.27×101 G: 1.84×101 H: 2.66×101 Tries 0/12

What is the pressure (in Pa)? (Assume an ideal fluid)

A: 8.24×105 B: 9.31×105 C: 1.05×106 D: 1.19×106 E: 1.34×106 F: 1.52×106 G: 1.72×106 H: 1.94×106

Answer 1

Density of water = = 1000 kg/m³

Cross-sectional area of the pipe at the first point = A₁ = 2.9 x 10^-2 m²

Pressure of the water at the first point = P₁ = 10.9 x 10⁵ Pa

Velocity of flow of water at the first point = V₁ = 0.31 m/s

Cross-sectional area of the pipe at the second point = A₂ = 10.3 x 10^-4 m²

Pressure of the water at the second point = P₂

Velocity of flow of water at the second point = V₂

By Continuity Equation,

V₂ = 8.73 m/s

The pipe is horizontal therefore the first and second points are at same height.

By Bernoulli's equation,

P₂ = 1.05 x 10⁶ Pa

a) Velocity of the water in the constricted region = 8.73 m/s

b) Pressure of the water in the constricted region = 1.05 x 10⁶ Pa