Question

A venturi meter is a device for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at a speed v2 through a horizontal section of pipe whose cross-sectional area A2 = 0.0800 m2. The gas has a density of rho = 1.20 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0300 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 140 Pa. Find the speed v2 of the gas in the larger original pipe. Find the volume flow rate Q of the gas.

Answer 1

Answer:

$V_2=6.17\ m/s$

$Q=0.49\ m^3/s$

Explanation:

Given that

$A_1=0.03m^2$

$A_2=0.08m^2$

We know that from continuity equation

$Q=A_1V_1=A_2V_2$

So

$A_1V_1=A_2V_2$

$0.3V_1=0.08V_2$

$V_1=2.66V_2$

Now from energy equation

$P_1+\dfrac{1}{2}\rho V_1^2=P_2+\dfrac{1}{2}\rho V_2^2$

$P_2-P_1=\dfrac{1}{2}\rho V_1^2-\dfrac{1}{2}\rho V_2^2$

$140=\dfrac{1}{2}\times 1.2\times 7.11\times V_2^2-\dfrac{1}{2}\times 1.2\times V_2^2$

$V_2=6.17\ m/s$

$Q=A_2V_2$

Q=6.17 x 0.08

$Q=0.49\ m^3/s$