Fluid Mechanics Investigation

[ConceptuallyInept]

(Thanks to the guy who answered my original thread)

For a physics project I'm investigating the effects on the flow rate of fluids. I'm going to find a relationship between orifice diameter and flow rate (keeping things simple I'll assume it's a circular orifice for a cylindrical can). For the empirical data I obtain, I've got to have theoretical support. If there's a genius out there who could tell me what law or relationship I need then I'd be very grateful.

 

[Gmaximus]

$$a_1v_1=a_2v_2$$
$$Flow Rate=Dav$$ Where D is density.
And look up "Bernoulli's Equation"

 

[M98Ranger]

Hi there,

Thank you for sharing your fluid mechanics investigation project with us. It sounds like a very interesting and practical experiment. I'm glad that someone was able to provide you with some helpful information in your original thread.

To answer your question, the law or relationship you need to use for your project is Bernoulli's Principle. This principle states that as the speed of a fluid increases, the pressure within the fluid decreases. In other words, as the velocity of the fluid increases, the pressure decreases. This can be seen in everyday examples such as the lift of an airplane wing or the flow of water through a narrow pipe.

In your investigation, you can use Bernoulli's Principle to explain the relationship between orifice diameter and flow rate. As the diameter of the orifice decreases, the velocity of the fluid passing through it will increase, leading to a decrease in pressure. This decrease in pressure will result in a higher flow rate.

To support your empirical data, you can use the Bernoulli equation, which is:

P1 + (1/2)ρv1^2 + ρgh1 = P2 + (1/2)ρv2^2 + ρgh2

Where:
P1 and P2 are the pressure at points 1 and 2
ρ is the density of the fluid
v1 and v2 are the velocities at points 1 and 2
g is the acceleration due to gravity
h1 and h2 are the heights at points 1 and 2

By using this equation, you can calculate the pressure and velocity at different points along the flow and see how they change with varying orifice diameters.

I hope this helps and good luck with your project! Don't forget to also consider factors such as fluid viscosity and surface tension that may also affect your results.