Question

A piston of cross sectional area 2cm2 pushes liquid out of a tube whose area at outlet is 40 mm2
.
Piston is pushed at 2cm/s. Find speed of fluid.​

Answer 1

Solution:

Piston of cross sectional area, A₁ = 2 cm²

Piston is pushed at speed, v₁ = 2 cm/s

Cross sectional area of tube, A₂ = 40 mm² = 40/10 = 0.4 cm²

Speed of fluid which is outgoing, v₂ = x cm/s [Let it be x]

We will apply Equation of Continuity here.

Equation of Continuity =>

A₁v₁ = A₂v₂

2 * 2 = 0.4 * x

x = 4/0.4

x = 10 cm/s

The speed of fluid which is outgoing will be 10 cm/s

The equation of continuity tells us about the moving of some quantity from one place to another. It needs to conserve the mass of volume element like volume element coming in equal amount as that of going out in equal amount.

Answer 2

Explanation:

Let A1 =2cm²= 2×10*-4

A2=40mm²=40×10*-6

v1 = 2cm=2×10*-2

v2=?

according to equation of continuity of fluids ,

A1v1 = A2v2

v2= A1v1 / A2

= 2× 10*-4 × 2× 10*-2 / 40×10*-6

= 0.1m/s

therefore v2 = 0.1m/s

Hope this helps you ❤