Question

Water flows through a horizontal tube of diameter 3.0 cm that is joined to a second horizontal tube of diameter 1.0 cm. The pressure difference between the tubes is 7.5 kPa.1. Find the speed of flow in the first tube.

Answer 1

v₁ = 0.433 m/s

Step-by-step explanation:

given,

diameter of first tube, d₁ = 3 cm

diameter of second tube, d₂ = 1 cm

Pressure difference= 7.5 kPa

using continuity equation

A₁ v₁ = A₂ v₂

`v_1=(\pi r_2^2)/(\pi r^2_1)v_2`

`v_1=(0.5^2)/(1.5^2)v_2`

v₂ = 9 v₁

Applying Bernoulli's equation

`\Delta P = (1)/(2)\rho (v_2^2-v_1^2)`

`7.5 * 10^3= (1)/(2)* 1000* ((9v_1)^2-(v_1)^2)`

80 v₁² = 15

v₁² =0.1875

v₁ = 0.433 m/s