Why Is P1A1 Considered Positive in Fluid Force Calculations?

In summary, the formula for the force exerted on the fluid by the pipe is P1A1 - Fx - P2A2. The P1A1 term represents the force exerted by the fluid behind the control volume on the fluid in the control volume, while -Fx is the force exerted by the pipe on the fluid. The -P2A2 term represents the force exerted by the fluid ahead of the control volume on the fluid in the control volume. This can be seen in the change in momentum due to the change in cross sectional area of the pipe.
  • #1
foo9008
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Homework Statement



The formula of the force exerted on the fluid by the pipe is P1A1 –Fx – P2A2 , I don’t understand why the P1A1 is positive ?

Homework Equations

The Attempt at a Solution



Assuming to the right is positive , shouldn’t the force acting on the water = -P1A1 ?

Because the water is flowing from left to right , the force acting on the water by the pipe should be in oppostite direction( which is –P1A1 ) , am I right ?
 
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  • #3
foo9008 said:
I don’t understand why the P1A1 is positive ?
as water is flowing to the right force exerted by pipe on water should be left to right=its perhaps helping the water to maintain the flow
Things don't just start moving by themselves. There must be a force acting on the water in the pipe for it to move, and the obvious one is its own weight. Water is quite heavy stuff - a litre of it weighs a kilogram. The water in the tank pushes down on the water in the pipe.
what is your Fx ?
it appears your pipe diameter is changing!
 
  • #4
drvrm said:
as water is flowing to the right force exerted by pipe on water should be left to right=its perhaps helping the water to maintain the flow
Things don't just start moving by themselves. There must be a force acting on the water in the pipe for it to move, and the obvious one is its own weight. Water is quite heavy stuff - a litre of it weighs a kilogram. The water in the tank pushes down on the water in the pipe.
what is your Fx ?
it appears your pipe diameter is changing!
if so , why F2 is in opposite direction ? according to you , F2 should help the water to flow , so it should in the same direction as the water flow , right ? which is directed to the right ?
 
  • #5
foo9008 said:
f so , why F2 is in opposite direction ? according to you , F2 should help the water to flow , so it should in the same direction as the water flow , right ? which is directed to the right ?

in previous post i did'nt see the diagram of 'reducer'... i think the contraption is pushing water through a nozzle of reduced diameter and its not a 'streamline flow' arrangement - the change in momentum is being presented as a force Fx-
so the water at the nozzle is being pushed as a 'reaction' of the volume of water being pushed to the right- its a macro-model made by the set up;
its something like pushing burnt gas out of nozzle of rocket and a back thrust .
 
  • #6
drvrm said:
in previous post i did'nt see the diagram of 'reducer'... i think the contraption is pushing water through a nozzle of reduced diameter and its not a 'streamline flow' arrangement - the change in momentum is being presented as a force Fx-
so the water at the nozzle is being pushed as a 'reaction' of the volume of water being pushed to the right- its a macro-model made by the set up;
its something like pushing burnt gas out of nozzle of rocket and a back thrust .
i still don't understand why the F1 is acting as the same direction of the low of water , can you explain further?
 
  • #7
drvrm said:
as water is flowing to the right force exerted by pipe on water should be left to right=its perhaps helping the water to maintain the flow
Things don't just start moving by themselves. There must be a force acting on the water in the pipe for it to move, and the obvious one is its own weight. Water is quite heavy stuff - a litre of it weighs a kilogram. The water in the tank pushes down on the water in the pipe.
what is your Fx ?
it appears your pipe diameter is changing!
or do you mean since the diameter is decreasing along the pipe , so the F1 is to help the water flow (since there is not much obstruction ) , F2 is the force which try to prevent the water flow (since the water is difficult to move thru smaller diameter of pipe), so it is in opposite direction?
 
  • #11
The expression you gave is not the force exerted by the pipe on the fluid. Only -Fx is the force exerted by the pipe on the fluid. P1A1 is the force exerted by the fluid behind the control volume on the fluid in the control volume, and -P2A2 is the force exerted by the fluid ahead of the control volume on the fluid in the control volume. Since the cross sectional area has changed, there also should be a rate of change of momentum term on the other side of the equation.
 
  • #12
Chestermiller said:
The expression you gave is not the force exerted by the pipe on the fluid. Only -Fx is the force exerted by the pipe on the fluid. P1A1 is the force exerted by the fluid behind the control volume on the fluid in the control volume, and -P2A2 is the force exerted by the fluid ahead of the control volume on the fluid in the control volume. Since the cross sectional area has changed, there also should be a rate of change of momentum term on the other side of the equation.
Why F1 is behind the control volume? F2 is ahead of control volume?
 
  • #13
foo9008 said:
Why F1 is behind the control volume? F2 is ahead of control volume?
If there is pressure within the fluid, the fluid behind exerts a forward force on the fluid ahead of it, and the fluid ahead exerts a backward force on the fluid behind it.
 
  • #14
Chestermiller said:
If there is pressure within the fluid, the fluid behind exerts a forward force on the fluid ahead of it, and the fluid ahead exerts a backward force on the fluid behind it.
Why, can you explain??
 
  • #15
foo9008 said:
Why, can you explain??
Are you aware of Pascal's Law that, at a given location in a fluid, pressure acts equally (isotropically) in all directions?
 
  • #16
Chestermiller said:
Are you aware of Pascal's Law that, at a given location in a fluid, pressure acts equally (isotropically) in all directions?
Yes, how is the condition above link to pascal law
 
  • #17
foo9008 said:
Yes, how is the condition above link to pascal law
Is there pressure in the fluid that is situated behind the fluid in the control volume? According to Pascal's Law, does it push forward on the fluid within the control volume? Is there pressure in the fluid that is situated ahead of the fluid in the control volume? According to Pascal's Law, does it push backwards on the fluid within the control volume?
 
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Related to Why Is P1A1 Considered Positive in Fluid Force Calculations?

1. What is the definition of force on a pressure pipe?

The force on a pressure pipe is the amount of external pressure or load exerted on the pipe, which can affect its structural integrity and ability to withstand pressure.

2. How is force on a pressure pipe calculated?

The force on a pressure pipe is typically calculated using the formula F = PA, where F is the force, P is the pressure exerted on the pipe, and A is the cross-sectional area of the pipe.

3. What factors can affect the force on a pressure pipe?

There are several factors that can affect the force on a pressure pipe, including the type of fluid or material being transported, the velocity of the fluid, the temperature, and the diameter and thickness of the pipe.

4. How can force on a pressure pipe be reduced?

To reduce the force on a pressure pipe, the pipe can be reinforced with additional support structures, such as struts or braces. Additionally, using a larger diameter or thicker pipe can also help to distribute the force more evenly.

5. What are the potential consequences of high force on a pressure pipe?

If a pressure pipe is subjected to high force, it can lead to structural damage, leaks, or even bursts. This can result in costly repairs, downtime, and potential safety hazards. Regular maintenance and monitoring can help to prevent excessive force on pressure pipes.

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