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

`V_2=6.17\ m/s`

`Q=0.49\ m^3/s`

Step-by-step 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+(1)/(2)\rho V_1^2=P_2+(1)/(2)\rho V_2^2`

`P_2-P_1=(1)/(2)\rho V_1^2-(1)/(2)\rho V_2^2`

`140=(1)/(2)* 1.2* 7.11* V_2^2-(1)/(2)* 1.2* 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`