# A1v1=a2v2? pressure and velocity are inversely proportional?

• Fizzizist
In summary, A1v1=a2v2 is a mathematical equation known as the continuity equation that explains the relationship between pressure and velocity in fluid systems. It states that as cross-sectional area decreases, velocity must increase to maintain a constant flow rate. This equation has practical applications in understanding and analyzing fluid behavior in various systems and is applicable to all types of fluids. It can also be used to calculate the velocity of a fluid and is closely related to Bernoulli's principle.
Fizzizist
If Bernoulli's equation P + 1/2ρv2 + ρgh = constant, implying that pressure decreases as velocity increases, and the Venturi effect states that a1v1 = a2v, what resolves this apparent contradiction? The velocity slows as the cross sectional area increases, but a narrower pipe would have greater pressure?

Fizzizist said:
There is no contradiction to resolve.

Fizzizist said:
The velocity slows as the cross sectional area increases, but a narrower pipe would have greater pressure?
You have this backwards. A larger pipe has greater pressure. That is why brain aneurysms are dangerous

## 1. How does A1v1=a2v2 explain the relationship between pressure and velocity?

A1v1=a2v2 is a mathematical equation known as the continuity equation, which states that the product of cross-sectional area and velocity at one point in a fluid system is equal to the product of cross-sectional area and velocity at another point. This equation shows that as the cross-sectional area decreases, the velocity must increase in order to maintain a constant flow rate. This explains the inverse relationship between pressure and velocity - as velocity increases, pressure decreases, and vice versa.

## 2. What is the practical application of A1v1=a2v2 in fluid dynamics?

The continuity equation is widely used in fluid dynamics to understand and analyze the behavior of fluids in various systems, such as pipes, pumps, and turbines. It helps engineers and scientists to predict the flow rate and pressure in these systems, which is crucial in designing and optimizing them for efficient and safe operation.

## 3. Is A1v1=a2v2 applicable to all types of fluids?

A1v1=a2v2 is a fundamental equation in fluid dynamics and is applicable to all types of fluids, including liquids and gases. However, in some cases, this equation may need to be modified to account for factors such as compressibility and viscosity of the fluid.

## 4. Can the continuity equation be used to calculate the velocity of a fluid?

Yes, the continuity equation can be rearranged to calculate the velocity of a fluid at a specific point. However, it is more commonly used to understand the relationship between pressure and velocity, rather than to directly calculate velocity.

## 5. How does A1v1=a2v2 relate to Bernoulli's principle?

Bernoulli's principle states that in a fluid flow, an increase in velocity results in a decrease in pressure, and vice versa. This is essentially the same relationship shown by A1v1=a2v2. In fact, the continuity equation is derived from Bernoulli's principle and can be seen as an extension of it to a more complex fluid system.

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