# Venturi Principle: Is p1=p3 and v1=v3?

• fonz
In summary, if the flow is inviscid and the cross sectional areas are the same, then p1=p3 and v1=v3. However, it cannot be determined if A1=A3 from the given diagram. Additionally, with zero viscosity, the inner flow at section 3 may not be determined and the average net flow v3 should be the same as v1, assuming the diameters at sections 1 and 3 are the same.
fonz

Just simply, from the diagram above is p1=p3 and v1=v3?

Thanks
Dan

If the viscosity is negligible, then yes.

If the cross sectional areas are the same and the flow is inviscid, then yes. From the diagram, it isn't certain that A1 = A3 though.

cjl said:
If the cross sectional areas are the same and the flow is inviscid, then yes.
If the flow is inviscid, then the inner flow at section 3 can't be determined. With zero viscosity, there's no reason that the flow from section 2 couldn't simply continue with the same diameter as the tube in section 2, flowing at v2 while the surrounding fluid in section 3 isn't moving at all, since there's no interaction between shear boundaries with an inviscid flow. The "average" net flow v3 should be the same as v1 since mass flow is constant, assuming section 3 diameter is the same as section 1 diameter.

According to the Venturi Principle, the pressure and velocity at points 1 and 3 are not necessarily equal. The principle states that as the velocity of a fluid increases, the pressure decreases. Therefore, at point 1 where the fluid is moving faster, the pressure will be lower compared to point 3 where the fluid is moving slower. Similarly, the volumes at points 1 and 3 may also not be equal, as the volume of a fluid can change with changes in pressure. However, the principle does state that the total energy at both points should be equal, meaning that the sum of the kinetic and potential energies should be the same.

## 1. What is the Venturi Principle?

The Venturi Principle is a scientific concept that states that as the velocity of a fluid increases, the pressure decreases.

## 2. How does the Venturi Principle work?

The Venturi Principle works by using a constricted tube or pipe to accelerate the fluid, which causes a decrease in pressure according to Bernoulli's principle. The pressure then returns to its original level after the fluid leaves the constriction.

## 3. Is p1=p3 and v1=v3 in the Venturi Principle?

Yes, according to the Venturi Principle, the pressure (p) at the entrance (1) and exit (3) of the constriction should be equal, as well as the velocity (v) at these points.

## 4. What are the applications of the Venturi Principle?

The Venturi Principle has many practical applications, such as in carburetors, where it is used to mix air and fuel in the correct ratio for combustion. It is also used in respiratory devices, water filtration systems, and even musical instruments.

## 5. Are there any limitations to the Venturi Principle?

While the Venturi Principle is a useful concept, it does have some limitations. It assumes that the fluid is incompressible and that there is no turbulence present. In reality, these conditions may not always be met, leading to discrepancies in the predicted pressure and velocity values.

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