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 = 0.0900 m2. The gas has a density of ñ = 1.50 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0600 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 190 Pa.

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 = 0.0900 m2. The gas has a density of ñ = 1.50 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0600 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 190 Pa.

Answer 1

There is no question here.

Answer 2

sorry i forgot to put the question

(a) Find the speed v2 of the gas in the larger original pipe.

(b) Find the volume flow rate Q of the gas.

Answer 3

To find the speed of the gas flowing through the Venturi meter, we can use Bernoulli's equation, which relates the pressure, velocity, and height of a fluid. Bernoulli's equation is given by:

P1 + 0.5 * ρ * v1^2 + ρ * g * h1 = P2 + 0.5 * ρ * v2^2 + ρ * g * h2

In this equation, P1 and P2 are the pressures at points 1 and 2, respectively, ρ is the density of the gas, v1 and v2 are the speeds of the gas at points 1 and 2, g is the acceleration due to gravity, and h1 and h2 are the heights at points 1 and 2, respectively.

Considering that the height is the same for both points, h1 = h2, and assuming that the acceleration due to gravity is negligible for horizontal flow, we can simplify the equation to:

P1 + 0.5 * ρ * v1^2 = P2 + 0.5 * ρ * v2^2

Since we are interested in finding the speed v2, we can rearrange the equation as:

v2^2 = ((P1 - P2) / ρ) + v1^2

We are given that P2 - P1 = 190 Pa, ρ = 1.50 kg/m3, v1 is not provided, and we need to find v2. However, we can use the principle of continuity, which states that the mass flow rate remains constant in steady state flow, to relate the speeds and areas of the gas at points 1 and 2.

The mass flow rate is given by:

m_dot = ρ * A * v

Since the mass flow rate remains constant, we can write:

ρ1 * A1 * v1 = ρ2 * A2 * v2

Rearranging this equation, we get:

v2 = (ρ1 * A1 * v1) / (ρ2 * A2)

Substituting the given values A1 = 0.0600 m2, A2 = 0.0900 m2, and ρ = 1.50 kg/m3, we can solve for v2.

Keep in mind that we still need the value of v1 to find v2. If v1 is not given in the problem, you won't be able to find v2 using the given information alone.