# Relationship of velocity to height and pressure

### What is Bernoulli's equation? (article) | Khan Academy

rate, velocity? i want to find the capacity of water Pump for building if it is 5 storied, 3/4 inch pipe, water density kg/m3. Water Pumps · Piping · Pressure . Distance, Velocity, Momentum, Force, Pressure, Work and Energy. Distance Work done to lift an object of mass m a height h: W = Fgh = mgh. Work done. For turbulent flow, the speed and or the direction of the flow varies. The pressure, speed, and height (y) at two points in a steady-flowing.

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.

Calculating height when you only know an object's final velocity

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. We can take the velocity to be zero at both points the acceleration occurs as the water rises up to ground level, coming from the difference between the chamber pressure and atmospheric pressure.

The pressure on the right-hand side is atmospheric pressure, and if we measure heights from the level of the chamber, the height on the left side is zero, and on the right side is 60 m.

Why curveballs curve Bernoulli's equation can be used to explain why curveballs curve. Let's say the ball is thrown so it spins. As air flows over the ball, the seams of the ball cause the air to slow down a little on one side and speed up a little on the other. The side where the air speed is higher has lower pressure, so the ball is deflected toward that side. To throw a curveball, the rotation of the ball should be around a vertical axis.

### Bernoulli's Equation

It's a little more complicated than that, actually. Although the picture here shows nice streamline flow as the air moves left relative to the ball, in reality there is some turbulence.

The air does exert a force down on the ball in the figure above, so the ball must exert an upward force on the air. This causes air that travels below the ball in the picture to move up and fill the space left by the ball as it moves by, which reduces drag on the ball. The flow therefore satisfies all the restrictions governing the use of Bernoulli's equation.

Upstream and downstream of the contraction we make the one-dimensional assumption that the velocity is constant over the inlet and outlet areas and parallel. One-dimensional duct showing control volume. When streamlines are parallel the pressure is constant across them, except for hydrostatic head differences if the pressure was higher in the middle of the duct, for example, we would expect the streamlines to diverge, and vice versa.

If we ignore gravity, then the pressures over the inlet and outlet areas are constant.

## What is Bernoulli's equation?

Along a streamline on the centerline, the Bernoulli equation and the one-dimensional continuity equation give, respectively, These two observations provide an intuitive guide for analyzing fluid flows, even when the flow is not one-dimensional. For example, when fluid passes over a solid body, the streamlines get closer together, the flow velocity increases, and the pressure decreases. Airfoils are designed so that the flow over the top surface is faster than over the bottom surface, and therefore the average pressure over the top surface is less than the average pressure over the bottom surface, and a resultant force due to this pressure difference is produced.

This is the source of lift on an airfoil.

Lift is defined as the force acting on an airfoil due to its motion, in a direction normal to the direction of motion. Likewise, drag on an airfoil is defined as the force acting on an airfoil due to its motion, along the direction of motion. An easy demonstration of the lift produced by an airstream requires a piece of notebook paper and two books of about equal thickness.

Place the books four to five inches apart, and cover the gap with the paper. When you blow through the passage made by the books and the paper, what do you see?

### Relationship between velocity and pressure of a fluid in motion - Physics Stack Exchange

Example 1 A table tennis ball placed in a vertical air jet becomes suspended in the jet, and it is very stable to small perturbations in any direction. Push the ball down, and it springs back to its equilibrium position; push it sideways, and it rapidly returns to its original position in the center of the jet.

In the vertical direction, the weight of the ball is balanced by a force due to pressure differences: To understand the balance of forces in the horizontal direction, you need to know that the jet has its maximum velocity in the center, and the velocity of the jet decreases towards its edges.

The ball position is stable because if the ball moves sideways, its outer side moves into a region of lower velocity and higher pressure, whereas its inner side moves closer to the center where the velocity is higher and the pressure is lower. The differences in pressure tend to move the ball back towards the center. Example 3 Suppose a ball is spinning clockwise as it travels through the air from left to right The forces acting on the spinning ball would be the same if it was placed in a stream of air moving from right to left, as shown in figure Spinning ball in an airflow.

A thin layer of air a boundary layer is forced to spin with the ball because of viscous friction. At A the motion due to spin is opposite to that of the air stream, and therefore near A there is a region of low velocity where the pressure is close to atmospheric.