# Pressure and velocity relationship of water

### fluid dynamics - Relation between pressure, velocity and area - Physics Stack Exchange Could anyone please tell about pressure and velocity relationship There are other systems where velocity is related to pressure, so please qualify on your .. analysis of a double pipe helical type heat exchanger using water as fluid. 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. A pump supplies water at 60 psi and 10 gpm through a pipe. If a valve on the pipe is slightly opened, a small stream of water shoots out. The pressure pushing . To understand the relationship between the pressure drop across a pipeline and the flow rate through that pipeline, we need to go back to one of the most important fundamental laws that governs the flow of fluid in a pipe: Total Fluid Energy Daniel Bernoulli, a Swiss mathematician and physicist, theorized that the total energy of a fluid remains constant along a streamline assuming no work is done on or by the fluid and no heat is transferred into or out of the fluid.

The total energy of the fluid is the sum of the energy the fluid possesses due to its elevation elevation headvelocity velocity headand static pressure pressure head. The energy loss, or head loss, is seen as some heat lost from the fluid, vibration of the piping, or noise generated by the fluid flow.

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

Between two points, the Bernoulli Equation can be expressed as: In other words, the upstream location can be at a lower or higher elevation than the downstream location. If the fluid is flowing up to a higher elevation, this energy conversion will act to decrease the static pressure. If the fluid flows down to a lower elevation, the change in elevation head will act to increase the static pressure. Conversely, if the fluid is flowing down hill from an elevation of 75 ft to 25 ft, the result would be negative and there will be a Pressure Change due to Velocity Change Fluid velocity will change if the internal flow area changes. For example, if the pipe size is reduced, the velocity will increase and act to decrease the static pressure.

If the flow area increases through an expansion or diffuser, the velocity will decrease and result in an increase in the static pressure. 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.

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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. At B, the direction of motion of the boundary layer is the same as that of the external air stream, and since the velocities add, the pressure in this region is below atmospheric. The ball experiences a force acting from A to B, causing its path to curve.

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

If the spin was counterclockwise, the path would have the opposite curvature. The appearance of a side force on a spinning sphere or cylinder is called the Magnus effect, and it well known to all participants in ball sportsespecially baseball, cricket and tennis players. 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. 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