There is no contradiction to resolve.Fizzizist said:what resolves this apparent contradiction?
You have this backwards. A larger pipe has greater pressure. That is why brain aneurysms are dangerousFizzizist said:The velocity slows as the cross sectional area increases, but a narrower pipe would have greater pressure?
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.
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.
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.
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.
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.