Question

A 7.5-cmcm-diameter horizontal pipe gradually narrows to 4.5 cmcm . When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 32.0 kPakPa and 25.0 kPakPa , respectively.

Answer 1

given,

diameter,d₁ = 7.5 cm

d₂ = 4.5 cm

P₁ = 32 kPa

P₂ = 25 kPa

Assuming, we have calculation of flow in the pipe

using continuity equation

A₁ v₁ = A₂ v₂

π r₁² v₁ = π r₂² v₂

`v_1= (r_2^2)/(r_1^2) v_2`

`v_1= (2.25^2)/(3.75^2) v_2`

`v_1= 0.36 v_2`

Applying Bernoulli's equation

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

`P_1-P_2 = (1)/(2)\rho (v_2^2-(0.36 v_2)^2)`

`32-25 = (1)/(2)1000* v_2^2 (1 - 0.1269)`

`v_2=\sqrt{(2* 7* 10^3)/(1000* (0.8704))}`

`v_2=√(16.084)`

v₂ = 4.01 m/s

fluid flow rate

Q = A₂ V₂

Q = π (0.0225)² x 4.01

Q = 6.38 x 10⁻³ m³/s

flow in the pipe is equal to 6.38 x 10⁻³ m³/s