Pressure in Fluids: Derivation & Explanation

In summary: Anyway, pressure does not vary along a line of constant height, but from the top downward, the pressure from the entire column of fluid presses down on the element, trying to push it down. The object holding the element up has to counteract this force PLUS the additional force per unit area arising from the weight of the fluid element itself, and hence the element feels a higher pressure at the bottom.
  • #1
Cheman
235
1
Pressure in fluids...

I have been looking at derivation of the equation Pressure in fluids= height of fluid column*density*gravitational field strength, from the intitial starting point of P = F/A and taking F to be weight of column. But I have since read that the pressure is not in fact due to the weight of the fluid but due to collisions between its molecules and some object, and that in fact the pressure acts from all directions, not just down. So if this is the case, then why does the equation I have previously mentioned hold, even for an upward or sideways pressure?

Thanks in advance. :wink:
 
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  • #2
At a certain height in water, the weight of the "column" of fluid above has to be supported by the fluid beneath it, because if the fluid is incompressible, it has nowhere to go. If everything is in equilibrium, it should be static. So indeed the net effect of that force due to pressure (all those collisions of molecules against each other) has to be to keep the fluid stationary. So consider that fluid element you were probably looking at in the derivation. The force on it has to be equal from the left side and from the ride side, otherwise it would have some net lateral motion. So we know pressure does not vary along a line of constant height. What about from above and from below? The force of the entire fluid column pressing down on top is indeed manifested as all those molecules colliding on the upper surface of that element, trying to push it down. It's weight is also trying to push it down. So the pressure from the bottom must be enough to counteract the pressure from the top PLUS the additional force per unit area arising from the weight of the fluid element itself. Hence, the pressure on the bottom is higher than at the top, so that the force on the bottom equals the downward force, keeping the element in equilibrium. Notice that only the forces can have direction, and are perpendicular to whatever surface we are considering them acting on. Pressure on the other hand, is just a property of the fluid at that particular height. It doesn't "act" from any direction. Force to due pressure on an immersed body does indeed act on the body from all sides. I hope this is somewhat comprehensible.
 
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  • #3
Cheman said:
I have been looking at derivation of the equation Pressure in fluids= height of fluid column*density*gravitational field strength, from the intitial starting point of P = F/A and taking F to be weight of column. But I have since read that the pressure is not in fact due to the weight of the fluid but due to collisions between its molecules and some object, and that in fact the pressure acts from all directions, not just down. So if this is the case, then why does the equation I have previously mentioned hold, even for an upward or sideways pressure?

Thanks in advance. :wink:

Let's say we were to stand under a 6 inch pipe running vertically to simulate a water column, and hold a piece of wood over our head to close off the bottom. Now as someone fills the pipe with a fluid from the top we notice that at first we can keep it from escaping by putting pressure against the pipe with the board...The more water we add to the column the more pressure we have to apply to the board to keep the water from escaping. The water pushes down on us and we push up. That same pressure pushes out (sideways) on the pipe too, with the bottom of the pipe feeling the most outward pressure.

Cheman said:
due to collisions between its molecules and some object,


I think this little bit is badly worded. You don't need to add some object; the pressure exists between the molecules themselves. I'm guessing it says object to refer to some kind of container or boundaries.
 

Related to Pressure in Fluids: Derivation & Explanation

1. What is pressure in fluids?

Pressure in fluids is the force exerted by a fluid per unit area. It is a measure of how much force is applied over a given area in a fluid. It is typically measured in units of Pascals (Pa) or pounds per square inch (psi).

2. How is pressure in fluids calculated?

Pressure in fluids is calculated by dividing the force exerted on a fluid by the area over which the force is applied. This is represented by the equation P = F/A, where P is pressure, F is force, and A is area.

3. What is the derivation of the equation for pressure in fluids?

The equation for pressure in fluids can be derived from the definition of pressure as force per unit area. By rearranging the equation P = F/A, we can see that pressure is equal to the force exerted over a given area. This relationship holds true for all fluids, including liquids and gases.

4. How does pressure in fluids change with depth?

Pressure in fluids increases with depth due to the weight of the fluid above. This is known as hydrostatic pressure and is described by the equation P = ρgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid.

5. What is the significance of pressure in fluids?

Pressure in fluids is an important concept in understanding the behavior of fluids. It helps explain why liquids and gases flow and how they exert forces on objects. Pressure in fluids also plays a crucial role in many applications, such as hydraulic systems and weather patterns.

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