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 ρ = 1.70 kg/m³. The Venturi meter has a cross-sectional area of A₁ = 0.0500 m² and has been substituted for a section of the larger pipe. The pressure difference between the sections is P₂ - P₁ = 130 Pa.

(a) Find the speed v₂ of the gas in the larger original pipe.
m/s
(b) Find the volume flow rate Q of the gas.

Answer 1

a)
let v1 and v2 are the speed of gas at two points.

Apply continuty equation, A1*v1 = A2*v2

v1 = v2*(A2/A1)

= v2*(0.08/0.05)

= 1.6*v2

now use< bernoullis' equation

P1 + (1/2)*rho*v1^2 = P2 + (1/2)*rho*v2^2

(1/2)*rho*(v1^2 - v2^2) = P2 - P1

(1/2)*rho*((1.6*v2)^2 - v2^2) = P2 - P1

(1/2)*rho*(1.56*v2^2) = P2 - P1

v2^2 = 2*(P2 - P1)/(1.56*rho)

v2 = sqrt(2*(P2 - P1)/(1.56*rho) )

= sqrt(2*130/(1.56*1.7) )

= 9.90 m/s <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<------Answer

b) volume flow rate, dVdt = A2*v2
= 0.08*9.90

= 0.792 m^3/s <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<------Answer