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.