Question

The pressure of water flowing through a 6.3×10^?2 ?m -radius pipe at a speed of 1.1 m/s is 2.2 ×105 N/m2.

(a) What is the flow rate of water?

(b) What is the pressure in the water after it goes up a 4.6 ?m -high hill and flows in a 5.0×10^?2 ?m-radius pipe?

Answer 1

a)

r = radius of pipe = 0.063 m

A = area of cross-section of the pipe = r² = (3.14) (0.063)² = 0.0125 m²

v = speed = 1.1 m/s

Flow rate is given as

V = Av = 0.0125 x 1.1 = 0.01375 m³/s

b)

A₁ = 0.0125 m²

v₁ = 1.1 m/s

A₂ =  area of cross-section of the pipe = r² = (3.14) (0.05)² = 0.00785 m²

v₂ = ?

using equation of continuity

A₁ v₁ = A₂ v₂

(0.0125) (1.1) = (0.00785) v₂

v₂ = 1.75

h₁ = 0

P₁ = 2.2 x 10⁵ N/m²

h₂ = 4.6 m

P₂ = ?

Using bernoulli's equation

P₁ + (0.5) v₁² + gh₁ = P₂ + (0.5) v₂² + gh₂

(2.2 x 10⁵)? + (0.5) (1000) (1.1)² + (1000) (9.8) (0) = P₂ + (0.5) (1000) (1.75)² + (1000) (9.8) (4.6)

P₂ = 1.74 x 10⁵ N/m²