Answer
given,
flow rate = p = 660 kg/m³
outer radius = 2.8 cm
P₁ - P₂ = 1.20 k Pa
inlet radius = 1.40 cm
using continuity equation
A₁ v₁ = A₂ v₂
π r₁² v₁ = π r₁² v₂
[tex]v_1= \dfrac{r_1^2}{r_2^2} v_2[/tex]
[tex]v_1= \dfrac{1.4^2}{2.8^2} v_2[/tex]
[tex]v_1= 0.25 v_2[/tex]
Applying Bernoulli's equation
[tex]\Delta P = \dfrac{1}{2}\rho (v_2^2-v_1^2)[/tex]
[tex]\Delta P = \dfrac{1}{2}\rho (v_2^2-(0.25 v_2)^2)[/tex]
[tex]\Delta P = \dfrac{1}{2}\rho v_2^2 (1 - 0.0625)[/tex]
[tex]v_2=\sqrt{\dfrac{2\Delta P}{\rho(1 - 0.0625)}}[/tex]
[tex]v_2=\sqrt{\dfrac{2\times 1200}{660 \times(1 - 0.0625)}}[/tex]
v₂ = 1.97 m/s
b) fluid flow rate
Q = A₂ V₂
Q = π (0.014)² x 1.97
Q = 1.21 x 10⁻³ m³/s
