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 = 0.0600 m2. The gas has a density of ñ = 1.30 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0400 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 190 Pa.
To find the speed of the gas flow (v2), we can use the Bernoulli's equation, which relates the pressure, velocity, and density of a fluid:
P1 + 1/2 * ρ * v1^2 = P2 + 1/2 * ρ * v2^2
Where:
P1 is the pressure at section 1 (before the Venturi meter)
P2 is the pressure at section 2 (after the Venturi meter)
ρ (rho) is the density of the gas
v1 is the velocity of the gas before the Venturi meter
v2 is the velocity of the gas after the Venturi meter
Given:
P2 - P1 = 190 Pa (pressure difference between the two sections)
A1 = 0.0400 m^2 (cross-sectional area of the Venturi meter)
A2 = 0.0600 m^2 (cross-sectional area of the larger pipe)
ρ = 1.30 kg/m^3 (density of the gas)
We can rearrange the equation to solve for v2:
v2^2 = (P1 - P2 + 1/2 * ρ * v1^2) * (2/ρ)
Substituting the values, we get:
v2^2 = (0 - 190 Pa + 1/2 * 1.30 kg/m^3 * v1^2) * (2/1.30 kg/m^3)
Simplifying further:
v2^2 = (-190 + 0.65 * v1^2) * 2/1.30
To calculate the actual speed of the gas flow (v2), we need to take the square root:
v2 = sqrt{(-190 + 0.65 * v1^2) * 2/1.30}
Please note that to solve for the velocity (v1) before the Venturi meter, we would need additional information like the pressure or diameter of the larger pipe or the flow rate of the gas.