Getting Qideal from Bernouli and continuity

The formula is derived from Bernoulli's principle and the principle of continuity. The person is seeking clarification on how to apply this formula in their lab report.
  • #1
Sheogoroth
2
0
So, I found a paper relating to a lab report that I've been working on that says that I can get
Qideal=(pi*d^2)/4) √((2ΔP/(ρ(1-D/D')^4 ))
From Bernouli which my book has as:
P1/ρ1+1/2v1^2+gh1=P2/ρ2+(1/2)v2^2+gh2

and Continuity which my book has as:
ρ1A1V1 = ρ2A2V2

I'm able to get kind of in that direction applying this,
ΔP = -ρgΔh

And the area portion makes sense logically

But I'm wondering what I'm missing.
Thanks!
 
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  • #2
The OP seems to be citing a relationship for calculating the volumetric flow rate across a resistance in the flow, such as an orifice plate based on the pressure difference across the resistance.
 

FAQ: Getting Qideal from Bernouli and continuity

What is the Bernoulli equation and how is it used in fluid dynamics?

The Bernoulli equation is a fundamental principle in fluid dynamics that relates the pressure, velocity, and elevation of a fluid in motion. It states that the total energy of a fluid remains constant along a streamline, meaning that when one of these variables changes, at least one other variable must also change to maintain the balance. This equation is used in various applications, such as calculating the lift force on an airplane wing or the flow rate through a pipe.

How does the continuity equation relate to the Bernoulli equation?

The continuity equation is another important principle in fluid dynamics that states that the mass flow rate of a fluid is constant, meaning that the amount of fluid entering a system must be equal to the amount of fluid leaving it. This equation is closely related to the Bernoulli equation, as it helps to determine how changes in pressure and velocity affect the flow of a fluid.

How can the Bernoulli equation be used to calculate the ideal fluid velocity?

The Bernoulli equation can be rearranged to solve for the ideal fluid velocity using the formula v = √(2(P1-P2)/ρ), where v is the velocity, P1 is the initial pressure, P2 is the final pressure, and ρ is the fluid density. This calculation assumes that the fluid is incompressible and that there is no energy loss due to friction or turbulence.

What is the significance of the ideal fluid assumption in the Bernoulli equation?

The ideal fluid assumption in the Bernoulli equation means that the fluid is assumed to have no viscosity, which is the internal resistance to flow. This assumption is necessary to simplify calculations and make the Bernoulli equation applicable to a wide range of fluid flow problems. However, in real-world situations, the ideal fluid assumption may not hold true, and factors such as viscosity and energy loss must be taken into account.

Can the Bernoulli equation be applied to all types of fluids?

The Bernoulli equation can be applied to any fluid, including liquids and gases, as long as the ideal fluid assumption holds true. However, for compressible fluids such as gases, the equation must be modified to account for changes in density due to changes in pressure. Additionally, for non-ideal fluids, the equation may need to be further adjusted to account for factors such as energy loss and viscosity.

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