# What is the fluid velocity in a restriction using Bernoulli's principle?

• fro
In summary, the conversation discusses the use of Bernoulli's principle to solve for fluid velocity in a restriction in a pipe, and the pressure in a wider section of the pipe when the radius is doubled. The equation A1v1 = A2v2 is used to solve for fluid velocity, and the conservation of mass equation is used to solve for pressure in the wider section.
fro
Liquid flows through a 4cm diameter at 1m/s. There is 2cm diameter restriction i n the line. Find fluid velocity in restriction.

$$p_1+ \rho\cdot g \cdot y_1 + \frac{1}{2}\rho \cdot(v_1)^2 = p_2+ \rho \cdot g\cdot y_2 + \frac{1}{2}\cdot \rho\cdot(v_2)^2$$

I know I have to use Bernoulli's principle to solve this. I am confused as to if I use the diameter or radius in the problem for the height. Can I cancel out p1 and p2?

Last edited:
Unless I'm missing something, you could solve this by simply stating A1v1 = A2v2, where A1 and A2 are the areas of the cross sections of the pipe.

Unless I'm missing something, you could solve this by simply stating A1v1 = A2v2, where A1 and A2 are the areas of the cross sections of the pipe.

Thanks, I got it.

Here is a slightly different one:
Water flows at 12m/s with pressure of 3X10^4 N/m^2. If the pipe widens to twice its original radius, what is the pressure in the wider section?

I am trying to plug everything to Bernoulli's principle. Problem is that both the pressure and radius is unknown. Any hints as to how I should start this problem? Thanks.

fro said:
Here is a slightly different one:
Water flows at 12m/s with pressure of 3X10^4 N/m^2. If the pipe widens to twice its original radius, what is the pressure in the wider section?

I am trying to plug everything to Bernoulli's principle. Problem is that both the pressure and radius is unknown. Any hints as to how I should start this problem? Thanks.

Again, use the equation (i.e. conservation of mass) you used to solve the first problem, and then you'll have everything you need to apply Bernoulli's equation and solve for the pressure in the wider section.

## 1. What is Bernoulli's principle?

Bernoulli's principle states that as the speed of a fluid increases, its pressure decreases. This principle is used to explain various phenomena, such as lift in airplanes and the function of carburetors.

## 2. Who discovered Bernoulli's principle?

It was discovered by the Swiss mathematician and physicist, Daniel Bernoulli, in the 18th century.

## 3. What is an example of Bernoulli's principle in action?

An example of Bernoulli's principle is the lift force acting on an airplane wing. As the speed of air increases over the curved upper surface of the wing, the pressure decreases, creating lift.

## 4. What factors affect the application of Bernoulli's principle?

The application of Bernoulli's principle is affected by the shape of the object, the speed of the fluid, and the density of the fluid.

## 5. Can Bernoulli's principle be applied to all types of fluids?

Bernoulli's principle can be applied to both liquids and gases, as long as the fluid is incompressible and the flow is steady and laminar.

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