Bernoulli's Principle with a Venturi Tube, find flow rate

[heatherro92]

So that's the question and I'm stuck on Part b. I don't even know how to approach it. I know A1= 3A2 but I don't know A1 and I need V2 and I don't know V1 or A2. I'm just confused as to how to do this. Please help!

 

[haruspex]

Are you aware of Bernoulli's equation? You mention Bernoulli in the title but don't quote the equation.

 

[heatherro92]

I understand the equation ρgy1+ (1/2)v1^2 + P1 =ρgy2+ (1/2)v2^2 + P2 but I do not understand how to apply it to this

 

[rcgldr]

I understand the equation ρgy1+ (1/2)v1^2 + P1 =ρgy2+ (1/2)v2^2 + P2 but I do not understand how to apply it to this

You need one more equation, based on the fact that mass flow within all parts of the venturi tube is constant.

 

[Nickie]

Part b of this question is asking you to find the flow rate using Bernoulli's Principle and a Venturi tube. To approach this problem, you will need to use the equation for Bernoulli's Principle, which states that the sum of the pressure, kinetic energy, and potential energy at any two points in a fluid flow system must remain constant.

To start, you know that A1 = 3A2, which means that the cross-sectional area of the first point is three times larger than the cross-sectional area of the second point. You also know that the flow rate is equal to the velocity multiplied by the cross-sectional area. This means that you can set up an equation using these variables:

Q = V1A1 = V2A2

Where Q is the flow rate, V1 and V2 are the velocities at the two points, and A1 and A2 are the cross-sectional areas at the two points.

To solve for the flow rate, you will need to find the values for V1 and V2. To do this, you can use the equation for Bernoulli's Principle, which includes the terms for pressure, kinetic energy, and potential energy.

P1 + 1/2ρV1^2 + ρgh1 = P2 + 1/2ρV2^2 + ρgh2

Where P1 and P2 are the pressures at the two points, ρ is the density of the fluid, g is the acceleration due to gravity, and h1 and h2 are the heights at the two points.

Since the fluid is assumed to be incompressible, the density ρ will cancel out of the equation. Also, since the two points are at the same height, the terms for potential energy will cancel out as well. This leaves you with the following equation:

P1 + 1/2V1^2 = P2 + 1/2V2^2

Now you can substitute the known values for P1, P2, and A1/A2 (since A1 = 3A2) into the equation and solve for V2. Once you have the value for V2, you can plug it back into the equation for the flow rate to find the final answer.

In summary, to approach this problem, you will need to use the equations for Bernoulli's Principle and the flow rate, and solve for the unknown variables by setting