# Bernoulli Equation VS. V1A1 = V2A2

• grandprix
In summary, the conversation discusses the use of the reduced V= sqrt (2gh) equation versus V1A1 = V2A2 in determining the velocity of a spigot located h meters in a tank. The reduced equation is used when the flow rate is forced to be the same, such as in a single pipe with no junctions. However, if the system is changed, the flow rate can also change, making the V1A1 = V2A2 equation not applicable. This is demonstrated by the example of two spigots with different cross sectional areas.
grandprix
Hi!

I came across a problem involving a spigot. In order to find the velocity in the spigot which is located h meters in the tank, one uses the reduced V= sqrt (2gh) equation... how is this different from using V1A1 = V2A2? When would you use this equation?

For instance, say you have a tank filled with a fluid with 2 spigots located at the same depth on each side of the container but spigot A has a larger cross sectional area than spigot B. According to my notes, the velocity will be the same in each but the flow rate will be greatest at A.

why wouldn't you use V1A1=V2A2 and say that spigot B would have a larger velocity given that it has a smaller cross sectional area?? I get that they used bernoullis for this one.. but i don't understand why the other equation wouldn't work either..

Because V1A1 = V2A2 only applies when the flow rate is forced to be the same (such as two different locations with different diameters along the same pipe). Since mass is conserved, you have to have the same mass flow rate in one place in a pipe as in any other place (assuming that it's just a single pipe, with no junctions). However, if you remove the pipe completely and replace it with a different pipe, you have changed the system. There is no particular reason why the flow rate of your new system has to be the same as for your old system, which is why that equation does not apply.

## 1. What is the Bernoulli Equation?

The Bernoulli Equation is a fundamental principle in fluid dynamics that relates the velocity, pressure, and height of a fluid at any two points in a flow. It states that the total energy of a fluid remains constant as it moves through a flow, neglecting any energy losses due to friction or viscosity.

## 2. What is V1A1 = V2A2?

V1A1 = V2A2 is the simplified form of the Bernoulli Equation, where V1 and V2 are the velocities at two different points in a flow, and A1 and A2 are the cross-sectional areas of the flow at those points. This equation demonstrates the inverse relationship between velocity and cross-sectional area in a flow, where an increase in velocity results in a decrease in cross-sectional area, and vice versa.

## 3. How is the Bernoulli Equation used in real-life applications?

The Bernoulli Equation is used in many real-life applications, such as in the design of airplane wings, pumps and turbines, and water flow in pipes. It is also used in weather forecasting and in understanding the flow of blood in the human body.

## 4. What are the assumptions made in the Bernoulli Equation?

The Bernoulli Equation assumes that the fluid is incompressible, inviscid (no internal friction), and is flowing at a steady state. It also assumes that the fluid is moving along a streamline, and that there are no energy losses due to friction or turbulence.

## 5. How does the Bernoulli Equation relate to the conservation of mass and energy?

The Bernoulli Equation is a direct result of the conservation of mass and energy. It states that the total energy of a fluid, which includes kinetic energy, potential energy, and pressure energy, remains constant as it flows through a system. This demonstrates the principle of conservation of energy, where energy cannot be created or destroyed, only transformed from one form to another.

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