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

Answer

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

 $v_1= \dfrac{r_2^2}{r_1^2} v_2$

 $v_1= \dfrac{2.25^2}{3.75^2} v_2$

 $v_1= 0.36 v_2$

Applying Bernoulli's equation

 $\Delta P = \dfrac{1}{2}\rho (v_2^2-v_1^2)$

 $P_1-P_2 = \dfrac{1}{2}\rho (v_2^2-(0.36 v_2)^2)$

 $32-25 = \dfrac{1}{2}1000\times v_2^2 (1 - 0.1269)$

 $v_2=\sqrt{\dfrac{2\times 7\times 10^3}{1000\times (0.8704)}}$

 $v_2=\sqrt{16.084}$

       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