How does dynamic pressure affect static pressure?

In summary, the question is about the net acting force on a round piston, with a 1 sq ft surface area, pushing water through a pipe at a constant velocity of 75 ft/sec. The diagram shows a vacuum behind the piston and a 37.9 psi dynamic pressure being generated by the flow. The question is whether the net acting force will be 2116.8 lbs, which is the pressure difference between the vacuum and the outside atmospheric pressure, or if the dynamic pressure or momentum of the flow will have any effect. The answer is that the dynamic pressure will not have an effect on the net force, as it only occurs when the velocity of a gas or fluid is changed. The pressure at the piston may be slightly
  • #1
rcoopster
12
0
I have attached another diagram, and in the diagram I show a round piston with a 1 sq ft surface area pushing water through the pipe out into to open atmosphere at 14.7 psi at a constant velocity of 75 ft/sec. There is a vacuum behind the piston, and I have calculated a 37.9 psi dynamic pressure being generated by the flow.

My question is: Based upon the dynamic pressure generated by the flow, the atmospheric outside the pipe, and the vacuum behind the piston plate, (ignoring the viscosity of the flow and the pipe walls) what will the net acting force be on the piston plate?

Will it simply be 2116.8 lbs, which is the pressure difference between the vacuum and the outside atmospheric pressure, or does the dynamic pressure or momentum of the flow have any affect?

Thank you,

rcoopster
 

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  • Dynamic and Static Pressure Diagram.JPG
    Dynamic and Static Pressure Diagram.JPG
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  • #2
Any Thoughts would be greatly appreciated, thanks!
 
  • #3
The dynamic pressure will not have an effect on the net force acting on the piston. Dynamic pressure effects only occur when the velocity of a gas or fluid is changed. If the velocity is constant, then dynamic pressure is just a number relative to some frame of reference. This is ingoring issues like friction with the walls of the pipe and viscosity in the water. In the real world, the pressure at the piston would have to be slightly greater than 1 atm, and pressure would decrease slightly with distance the water travels in the pipe due to friction and viscosity.
 
  • #4
Does this mean that the net acting force on the piston would be equal to the 2116.8 lb atmospheric pressure difference?

thanks,

Rcoopster
 
  • #5


I can explain the relationship between dynamic pressure and static pressure and how it affects the net acting force on the piston plate in your setup. Dynamic pressure is the force per unit area that is generated by a fluid in motion, while static pressure is the force per unit area that is exerted by a fluid at rest.

In your setup, the dynamic pressure is being generated by the flow of water through the pipe, while the static pressure is the atmospheric pressure outside the pipe and the vacuum behind the piston plate. Since the flow is at a constant velocity, the dynamic pressure will also remain constant at 37.9 psi.

Now, in order to determine the net acting force on the piston plate, we need to consider the forces acting on it. The atmospheric pressure will exert a force of 14.7 psi on the piston plate, while the vacuum behind it will exert a force of -37.9 psi (since it is a vacuum, the pressure is negative). This means that the net pressure acting on the piston plate is 14.7 psi + (-37.9 psi) = -23.2 psi.

However, we also need to consider the momentum of the flow. The flow of water has a certain mass and velocity, which means it also has momentum. This momentum will contribute to the net acting force on the piston plate. In order to calculate this force, we need to use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is the change in velocity over time, which is equal to the velocity (75 ft/sec) divided by the time it takes for the water to reach the end of the pipe.

Therefore, the net acting force on the piston plate will be the sum of the pressure force and the momentum force. It will not simply be 2116.8 lbs (the pressure difference between the vacuum and atmospheric pressure), but it will also include the force due to the momentum of the flow.

In conclusion, the net acting force on the piston plate will be affected by both the pressure difference and the momentum of the flow. It is important to consider both factors in order to accurately calculate the net force on the piston plate in your setup.
 

1. How does dynamic pressure affect static pressure?

Dynamic pressure is the force per unit area exerted by a moving fluid, while static pressure is the force per unit area exerted by a stationary fluid. When dynamic pressure increases, it causes an increase in the velocity of the fluid, which in turn causes a decrease in static pressure.

2. Can dynamic pressure and static pressure be equal?

No, dynamic pressure and static pressure cannot be equal as they represent two different types of pressure in a fluid. However, both pressures can be combined to calculate the total pressure of the fluid using the Bernoulli's equation.

3. How does the shape of an object affect the dynamic and static pressures?

The shape of an object can affect the dynamic and static pressures by changing the flow of the fluid around it. For example, a streamlined shape will cause the fluid to flow smoothly, resulting in a lower dynamic pressure and higher static pressure. On the other hand, a blunt shape will cause the fluid to flow turbulently, resulting in a higher dynamic pressure and lower static pressure.

4. What is the relationship between dynamic and static pressure in a fluid?

The relationship between dynamic and static pressure in a fluid is inverse. As dynamic pressure increases, static pressure decreases, and vice versa. This is because an increase in the velocity of the fluid causes a decrease in its pressure and vice versa.

5. How is dynamic pressure measured?

Dynamic pressure can be measured using a device called a pitot tube, which has one opening facing the direction of the fluid flow and another opening perpendicular to the flow. The difference in pressure between these two openings is a measure of the dynamic pressure of the fluid.

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