# Pressure and velocity relationship in fluids physics

### Bernoulli’s Effect – Relation between Pressure and Velocity - Nuclear Power

The equation of continuity states that for an incompressible fluid flowing The pressure, speed, and height (y) at two points in a steady-flowing. It is one of the most important/useful equations in fluid mechanics. It puts into a relation pressure and velocity in an inviscid incompressible flow. Bernoulli's. The higher the velocity of a fluid (liquid or gas), the lower the pressure it exerts. This is called Bernoulli's Principle. Fluid pressure is caused by.

## Bernoulli’s Effect – Relation between Pressure and Velocity

The idea that regions where the fluid is moving fast will have lower pressure can seem strange. Surely, a fast moving fluid that strikes you must apply more pressure to your body than a slow moving fluid, right?

Yes, that is right. But we're talking about two different pressures now. The pressure that Bernoulli's principle is referring to is the internal fluid pressure that would be exerted in all directions during the flow, including on the sides of the pipe.

**11th Class Physics, Ch 6 - Relation Between Speed & Pressure Fluid - FSc Physics Book 1**

This is different from the pressure a fluid will exert on you if you get in the way of it and stop its motion. I still don't get the difference.

### fluid dynamics - Relation between pressure, velocity and area - Physics Stack Exchange

Is the pressure higher or lower in the narrow section, where the velocity increases? Your first inclination might be to say that where the velocity is greatest, the pressure is greatest, because if you stuck your hand in the flow where it's going fastest you'd feel a big force. The force does not come from the pressure there, however; it comes from your hand taking momentum away from the fluid.

The pipe is horizontal, so both points are at the same height. Bernoulli's equation can be simplified in this case to: The kinetic energy term on the right is larger than the kinetic energy term on the left, so for the equation to balance the pressure on the right must be smaller than the pressure on the left.

It is this pressure difference, in fact, that causes the fluid to flow faster at the place where the pipe narrows. A geyser Consider a geyser that shoots water 25 m into the air. How fast is the water traveling when it emerges from the ground?

If the water originates in a chamber 35 m below the ground, what is the pressure there? To figure out how fast the water is moving when it comes out of the ground, we could simply use conservation of energy, and set the potential energy of the water 25 m high equal to the kinetic energy the water has when it comes out of the ground. Another way to do it is to apply Bernoulli's equation, which amounts to the same thing as conservation of energy.

Let's do it that way, just to convince ourselves that the methods are the same. But the pressure at the two points is the same; it's atmospheric pressure at both places. We can measure the potential energy from ground level, so the potential energy term goes away on the left side, and the kinetic energy term is zero on the right hand side.

This reduces the equation to: The density cancels out, leaving: This is the same equation we would have found if we'd done it using the chapter 6 conservation of energy method, and canceled out the mass.

To determine the pressure 35 m below ground, which forces the water up, apply Bernoulli's equation, with point 1 being 35 m below ground, and point 2 being either at ground level, or 25 m above ground.

Let's take point 2 to be 25 m above ground, which is 60 m above the chamber where the pressurized water is. Stagnation pressure and dynamic pressure Bernoulli's equation leads to some interesting conclusions regarding the variation of pressure along a streamline. Consider a steady flow impinging on a perpendicular plate figure There is one streamline that divides the flow in half: Along this dividing streamline, the fluid moves towards the plate.

### Bernoulli's Equation

Since the flow cannot pass through the plate, the fluid must come to rest at the point where it meets the plate. Bernoulli's equation along the stagnation streamline gives where the point e is far upstream and point 0 is at the stagnation point.

It is the highest pressure found anywhere in the flowfield, and it occurs at the stagnation point. It is called the dynamic pressure because it arises from the motion of the fluid.

The dynamic pressure is not really a pressure at all: Pitot tube One of the most immediate applications of Bernoulli's equation is in the measurement of velocity with a Pitot-tube.

The Pitot tube named after the French scientist Pitot is one of the simplest and most useful instruments ever devised. It simply consists of a tube bent at right angles figure Pitot tube in a wind tunnel. By pointing the tube directly upstream into the flow and measuring the difference between the pressure sensed by the Pitot tube and the pressure of the surrounding air flow, it can give a very accurate measure of the velocity.

Bernoulli's equation along the streamline that begins far upstream of the tube and comes to rest in the mouth of the Pitot tube shows the Pitot tube measures the stagnation pressure in the flow.

The density can be found from standard tables if the temperature and the pressure are known.