Question

A 30cm diameter pipe carries oil of specific gravity 0.8 at a velocity of 2m/s. At another section the diameter is 20cm. Find the velocity at this section and also mass rate of flow of oil

Answer 1

The velocity is 4.5 m/s and mass rate flow is  Δm / Δt  = 113 . 097 kg / s

Explanation:

We are given that:

• Diameter of pipe "d1" = 30 cm=0.3
• C/S Area of pipe 1 = A1  =  π(d1)^2 / 4 = 0.0225  πm^2  
• Diameter of pipe d2 = 20 cm = 0.2 m
• C/S Area of pipe = A2 = π(d2)^2 / 4 = 0.01  πm^2  
• Velocity at pipe 1 v(1)  =2 m/s
• Velocity at pipe 2 (v2) = ?

The rate of discharge through pipe 1 = Q1 = A1v1 = 0.0225 x 2 = 0.045 πm^3 / s = 0.1414 m^3 / s

From the equation of continuity Q1 = Q2 + Q3

Q1 = 0.045 πm^3 / s

Velocity = Q2 / A2 = 0.045  πm^3 / s / 0.01 πm^2 = 4.5 m/s  

Mass rate flow = Δm / Δt = 0.8 x 1000 kg / m^3 (0.045 m^3/s)

Δm / Δt  = 113 . 097 kg / s