# Relationship between velocity and pressure in fluids

### What is the relationship between pressure and velocity for a liquid and gas? | How Things Fly

In a wide range of fluids the pressure (in fact the entire stress tensor) is often a function of there is inverse relationship between P and v as by Bernoulli's eq. This is what Bernoulli's equation does, relating the pressure, velocity, and height of a fluid at one point to the same parameters at a second. Pressure/velocity variation. Consider the steady, flow of a constant density fluid in a converging duct, without losses due to friction (figure 14). The flow therefore.

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.

### Pressure - Velocity relation in fluids | CrazyEngineers

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.

## Flow in pipe - diameter, velocity, Reynolds number, Bernoulli equation, friction factor

When you blow through the passage made by the books and the paper, what do you see? 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 View calculator where is: With some restrictions, Darcy equation can be used for gases and vapors.

Darcy formula applies when pipe diameter and fluid density is constant and the pipe is relatively straight. Friction factor for pipe roughness and Reynolds number in laminar and turbulent flow Physical values in Darcy formula are very obvious and can be easily obtained when pipe properties are known like D - pipe internal diameter, L - pipe length and when flow rate is known, velocity can be easily calculated using continuity equation.

The only value that needs to be determined experimentally is friction factor. In the critical zone, where is Reynolds number between andboth laminar and turbulent flow regime might occur, so friction factor is indeterminate and has lower limits for laminar flow, and upper limits based on turbulent flow conditions.

If the flow is laminar and Reynolds number is smaller thanthe friction factor may be determined from the equation: Higher the water column higher the pressure. It is only the pressure acting at the particular height which causes the water to flow out as soon as it finds an opening and the constrain is removed the hole in this case.

### Fluid dynamics and Bernoulli's equation

There is nothing as reacting to the forces, the pressure is equal in ALL directions it is not unidirectional as any other stresses are, thats Pascals Law. Shear is not constant in fluids, e. Shear in laminar flows is linear, relative to vortical flow which isn't I have never said that the shear is constant.

And yes you are right, shear does exsist between the layers of water in a Vortex flow too. Stress at the inside walls of the container is "absorbed" into shear by the fluid motion. Flow is slower at the edges, because there is more friction and interaction, the flow is almost linear near the center, less linear near the walls. It is correct that the flow is slower at the edges due to friction between the fluid molecules in immediate contact with the surface, and this is exactly what causes the VELOCITY PROFILE in the fluid flow where the velocity is maximum at the center line of flow and lowest at the edges.

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

But there is nothing such as absorbing of the stresses being absorbed into shear. The flow is by the virtue of the driving force and the shear is merely the resistance to flow.

The centrally-directed flow 'pulls' the outer fluid along, translating normal stress into shear velocity It is not the inner flow which pulls the outer fluid, but in fact the nature of the velocity profile is itself dictated by the friction between the outer molecules, and the velocity goes on increasing from outside to inside as the friction goes on reducing towards the centre.

Correct, there is no shear in a static fluid, except Brownian Motion in molecules. Gas flowing down a pipe has two kinds of pressure, the gas pressure which varies and the flow rate which also varies locally, like a fluid'swhich is determined by both pressures and the cross section.