Question

A Venturi tube may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline (p = 660 kg/m³) through a hose having an outlet radius of 2.80 cm. If the difference in pressure is measured to be P1 - P2 = 1.20 kPa and the radius of the inlet tube to the meter is 1.40 cm.(a) Find the speed of the gasoline as it leaves the hose.(b) Find the fluid flow rate in cubic meters per second.

Answer 1

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

 $v_1= \dfrac{r_1^2}{r_2^2} v_2$

 $v_1= \dfrac{1.4^2}{2.8^2} v_2$

 $v_1= 0.25 v_2$

Applying Bernoulli's equation

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

 $\Delta P = \dfrac{1}{2}\rho (v_2^2-(0.25 v_2)^2)$

 $\Delta P = \dfrac{1}{2}\rho v_2^2 (1 - 0.0625)$

 $v_2=\sqrt{\dfrac{2\Delta P}{\rho(1 - 0.0625)}}$

 $v_2=\sqrt{\dfrac{2\times 1200}{660 \times(1 - 0.0625)}}$

       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