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 = 1.70 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 = 140 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 = 0.0600 m2. The gas has a density of ñ = 1.70 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 = 140 Pa.

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

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

anything would help. i have asked everyone and they don't know either.

Answer 1

Try to use P2-P1 = ρ/2(v1^2-v2^2)

Derived from P1 + 1/2ρv1^2 = P2 + 1/2ρv2^2

Then A1V1 = A2V2 is from continuity and can be expressed V1 = A2V2/A1

You get the equation P2 - P1 = ρ/2((A2V2/A1)^2 - V2^2) via substitution

And then simplify to 2(P2-P1)/ρ = A2V2/A1 - V2^2

Plug in and solve

Answer 2

To find the speed of the gas (v2) in the larger original pipe and the volume flow rate (Q) of the gas, we can use the principle of continuity and Bernoulli's equation.

Let's start with finding the speed of the gas (v2).

Step 1: Apply the principle of continuity:
The principle of continuity states that the volume flow rate of an incompressible fluid is constant along a pipe.
Q = A1 * v1 = A2 * v2
Where Q is the volume flow rate, A1 and A2 are the cross-sectional areas at two different points, and v1 and v2 are the speeds at those points.

Step 2: Rearrange the equation for v2:
v2 = (A1/A2) * v1

Step 3: Substitute the given values:
A1 = 0.0400 m^2
A2 = 0.0600 m^2

To continue, we need the value of v1. Unfortunately, it is not given in the problem statement. So we have to find v1 using Bernoulli's equation.

Step 4: Apply Bernoulli's equation:
P1 + (1/2) * ñ * v1^2 = P2 + (1/2) * ñ * v2^2
Where P1 and P2 are the pressures at two different points, ñ is the density of the gas, and v1 and v2 are the speeds at those points.

Step 5: Rearrange the equation for v1:
v1 = sqrt((2(P2 - P1))/ñ)

Step 6: Substitute the given values:
P2 - P1 = 140 Pa
ñ = 1.70 kg/m^3 (density of the gas)

Now we can substitute the obtained values of v1, A1, and A2 into the equation from Step 2 to find v2.

Finally, to find the volume flow rate (Q), substitute the obtained value of v2 into the equation from Step 1.

Note: Make sure to convert the units to match the given values.

I hope this explanation helps you solve the problem.