# If pressure is caused by the weight of water above you, why is pressure said to act in all direction, not just down?

I don’t think I have worded my question very well. Here’s another try…

We are taught that pressure of a fluid increases with depth, usually given the explanation of the increasing weight from the column of water above our object as it goes deeper. Then suddenly, we are taught that pressure acts in ALL direction. There’s a gap between those two explanations for me.

The column of water makes sense for pressure acting down and up on an object (like a rectangular box). But what about the sides of the box? There is not column of water there to explain why the pressure there should be just as high. How would you explain that?

And I am asking that how did the horizontal force force come if gravity is in vertical direction If by any means horizontal force comes what's the reason that horizontal force and vertical due to pressure by gravity are equal

• Due to conservation of momentum, pressure ALWAYS acts at right angles to the surface that it contacts. Example: bounce a ball against a flat wall. The fact that the angle of incidence equals the angle of reflection indicates that the force applied to the ball was perpendicular to the wall. In other words, the velocity component of the ball that was parallel to the wall did not change during the collision. Commented Aug 12 at 0:40
• Can you lift a tall column of water, as if it was made of stone? Can you topple it? Put it back where it was? Solid objects have these properties. Commented Aug 12 at 6:05
• I think you need to step back and consider how forces can be translated into a different direction. Imagine you are on a slight incline and pushing on a heavy cart to prevent it from rolling away. The cart is pushing against you with some horizontal force, right? But that force is coming from gravity which, as you say, is vertical. Commented Aug 12 at 17:43
• @Reznik Pressure still increases with depth in Jyothi's understanding, so in this view, you would still be pushed up, which is correct. Commented Aug 13 at 9:58

A fluid (n.) is fluid (adj.). It can change shape arbitrarily and flows to fill whatever space is available to it.

Fill a vertical cylindrical vessel with water. Drill a hole in the side near the bottom. Does water come out of that hole? Yes, of course. If pressure only produced vertical forces, there would be nothing to push the water through the horizontal hole, and that wouldn't happen.

The fluid nature of fluids means that when you push on them in one direction, they can "try to escape" by moving transverse to the direction of your push, and this puts pressure on whatever is to the side of the fluid, whether it's the wall of the vessel they're contained in or just another volume element of the fluid being pushed on.

If water was made of thin vertical rods, pressure would act like you said. The force on any patch would be the weight of the rods above. Force would not be transmitted sideways.

Water is made of tiny bouncing balls (molecules are close enough to ball shaped for this explanation.) If you press down on a ball, it might press sideways on the ball next to it. And that ball might press upward on its neighbor.

• Ball shape is less important than the fact that they are bouncing, because bouncing already removes the static friction to the sideways motion. Commented Aug 10 at 18:19
• If by any means horizontal force comes what's the reason that horizontal force and vertical due to pressure by gravity are equal Commented Aug 12 at 17:06
• If a fluid is at rest, the total force on each small piece of it is $0$. You can use this to show that pressure is the same in all directions. Pressure at a point is same in all directions in fluid | Proof Commented Aug 12 at 19:41
• Intuitively, suppose you press on the top and bottom of a small cube. You would squish it flat unless you pressed equally strongly on the sides. Commented Aug 12 at 19:58

Consider a big cylindrical tank of water. If you drill a hole in the bottom, water obviously comes out. If you drill a hole in the sides near the bottom, water comes out. If you take one of these side holes and put a pipe into it and then a 90 degree elbow pointing up, water will still come out. So the pressure will force water out in every direction, depending only on the height of the water (neglecting ambient pressure).

Another similar thought experiment is this: Say the tank is rectangular instead of cylindrical. Is some force required to hold the walls of the tank in place? The answer is yes. So the water must somehow "push" sideways as well as down.

If the water was solid, the answers to the above would be different. But we are considering a liquid and not a solid. That's the difference.

Addendum: Most students are familiar with the concept of elastic modulus $$E$$ that relates stress to strain for a small material component. Similarly, solid materials have a shear modulus (typically $$G$$) that relates moment to rotational strain. One defining characteristic of liquids is that their shear modulus is equal to ZERO, i.e. they cannot support a torque or shear (statically, anyway).

So, if we imagine the 2D state of a small piece of liquid under vertical forces it is typically represented like this:

where, $$\tau_{xy}$$ is zero for reasons explained. The stresses are shown in tension but obviously liquids can't support that. So think of the stress arrows as showing compression (pressure) instead. For the moment, let's also assume $$\sigma_x$$ is also zero and see what goes wrong.

Now if we can cut out a square piece of liquid and replace it by the outside forces, we can do the same for a triangular piece.

But now, see the problem? The picture shows them, but we actually can't allow any shear forces. So the only way to balance forces on this shape is to have a normal stress $$\sigma_n$$. Which in turn requires a horizontal stress $$\sigma_x$$.

This argument is shown in 2D but I think extends into 3D fairly obviously.

Pics lifted from "Transformations of Stress and Strain," D. Roylance, MIT, and Wikipedia website on Mohr's circle.

• I am asking that how did the horizontal force force come if gravity is in vertical direction Commented Aug 10 at 15:32
• Ah OK I think I can answer that, will edit my previous response. Commented Aug 10 at 15:38
• If by any means horizontal force comes what's the reason that horizontal force and vertical due to pressure by gravity are equal Commented Aug 10 at 15:53
• See addendum to my answer. Do the force balance on the triangular shape with $\sigma_y$, $\sigma_n$, and $\sigma_x$. To turn stresses into forces, they need to be multiplied by the relative length of the section which is a function of $\theta$. You should find that $\sigma_x = \sigma_y$ for any $\theta$. Commented Aug 10 at 16:13

Think of the cause-and-effect as, molecules bounce in all directions, creating something we call "pressure" which acts in all directions. Gravity is balanced by a pressure gradient, so the pressure rises until it balances gravity. But this is slightly different from saying "pressure is caused by gravity:" the source of pressure is bouncing particles in all directions.

Pressure of a fluid increases with depth

In the presence of a gravitational field aligned with "depth" in hydrostatic equilibrium, yes!

pressure acts in ALL direction

Yes. This is more fundamental. Typically, pressure is caused by the microscopic bouncing of particles (atoms, molecules, for example) in all directions. Pressure is fundamentally caused by bouncing in all directions, and thus equal. In balance, pressure rises up to meet the challenge posed by gravity.

How to bridge the gap?

The bridge between the two is pressure gradient, which you can think of the slope of the pressure. To balance gravity, a pressure gradient must exist. If you think of "slope", "gradient," "difference" as all being related, you can understand that a pressure gradient is necessary to produce a difference in forces, and thus a net force due to pressure.

Imagine a cube of water in the ocean. On all sides, pressure is acting. However, the front/back/left/right all balance out: there is pressure from the same height but in opposite directions. So there is no net force horizontally (and gravity also is not acting horizontally).

But vertically there is gravity. For this cube of water to be in force balance, there must be a net force upwards. So the pressure pushing up must be larger than the pressure pushing down. So the pressure at lower depth must be larger than the pressure at higher depth.

If you add together all the pressure gradients (or differences) of each cube of water stacked up, then the pressure at a given height is the weight of all the water above. You can think of this as either a sum or an integral.

• I am asking that how did the horizontal force force come if gravity is in vertical direction Commented Aug 12 at 16:55
• If by any means horizontal force comes what's the reason that horizontal force and vertical due to pressure by gravity are equal Commented Aug 12 at 16:56
• Typically, pressure is caused by the microscopic bouncing of particles (atoms, molecules, for example) in all directions. Pressure is fundamentally caused by bouncing in all directions, and thus equal. In balance, pressure rises up to meet the challenge posed by gravity. Thus, pressure gradient rises. Commented Aug 12 at 20:26
• 'Pressure is fundamentally caused by bouncing' in this it is applicable only to gases but not liquid. And pressure can also be created by gravity Commented Aug 13 at 1:40
• That's the fundamental misunderstanding you need to overcome if you want to understand the answer to your question. Pressure applies to fluids in general. Hydrostatic equilibrium can require a large pressure, but "what is" pressure? Fundamentally, bouncing in all directions. Commented Aug 13 at 3:13

$$\dots$$ we are taught that pressure acts in ALL direction.
Pressure does not have a direction as it is a scalar quantity.

The column of water makes sense for $$\bf \overbrace{pressure}^{\text{should be force}}$$ acting down and up on an object (like a rectangular box). But what about the sides of the box?

Here is the sort of diagram which may have made you make your incorrect assertion that pressure acts in all directions?

However you might then find that the text accompanying the diagram will say, the arrows adjacent to pressure labels PL, PR, PT, etc, indicate the directions of the forces on the sides of the element and PL, PR, PT, etc, indicate the magnitude of the pressure at the sides.

If the fluid is not to move horizontally each element of fluid in a horizontal strip will have a net zero horizontal force acting on it with the horizontal forces acting on an element either due to adjacent elements of fluid or due to the solid walls which contain the fluid.

• I am asking that how did the horizontal force force come if gravity is in vertical direction Commented Aug 12 at 16:56
• If by any means horizontal force comes what's the reason that horizontal force and vertical due to pressure by gravity are equal Commented Aug 12 at 17:03
• And if I remove both the opposite side forces the water is still in equilibrium Commented Aug 12 at 17:04
• @JyothiSrivalli Not at all in that the extreme fluid elements will have a net force on each of them. Commented Aug 12 at 20:32

The reason behind this is that water molecules do not simply stack on top of each other neatly; on the contrary, they are rather disordered.
As each individual molecule is pulled downwards by gravity, the water molecules near the bottom of the container are packed more tightly; due to the intermolecular repulsion, the distance of a molecule to the molecule on top will on average be equal to a molecule to its side; it is this intermolecular repulsion that creates the pressure.

• "the water molecules near the bottom of the container are packed more tightly". What do you mean? Water is almost incompressible (unless you apply truly enormous pressure). The density in a column of water (of constant temperature) is virtually uniform, despite the increase in pressure with depth. Commented Aug 11 at 10:57
• From hyperphysics.phy-astr.gsu.edu/hbase/permot3.html At the bottom of the Pacific Ocean at a depth of about 4000 meters, the pressure is about $\rm{4 × 10^7 \, N/m^2}$. Even under this enormous pressure, the fractional volume compression is only about 1.8% Commented Aug 11 at 11:14
• I never said that the change in intermolecular distance is large Commented Aug 11 at 12:10
• @PM2Ring I'm not sure that matters. Water is "almost incomprehensible" because it produces enormous forces when even slightly compressed. The "almost incomprehensible" and "enormous forces" cancel out and you can think about it from a compression perspective (even if the percentage compression is tiny) Commented Aug 11 at 14:30
• I am asking that how did the horizontal force force come if gravity is in vertical direction Commented Aug 12 at 16:56

Basically it's because water is a fluid and it flows around corners, so when it squeezes on you it squeezes from all directions.

Simply put: Because the pressure holds the water above!

Newton says: For any force, there is a opposite force equal strength. That's required to keep the total impulse constant. In the case of the water above you, it is pushing down on anything below it. But the water below is pushing back up with exactly the same force. Otherwise, the water column would be accelerating up- or downwards.

Or, considering that the water column is actually accelerated downwards by the force of gravity, there must be a force on the water that keeps it from falling down. And that force is supplied by the pressure gradient: Since every infinitesimally thin layer of water has a proportionally infinitesimally small weight, the force that pushes the layer up from below must be slightly stronger than the force that pushes down from above. As such, pressure grows as you move downwards, since more and more layer of water above you add to the pressure where you are and need to be carried by the water layers below.

• I am asking that how did the horizontal force force come if gravity is in vertical direction Commented Aug 12 at 17:02
• If by any means horizontal force comes what's the reason that horizontal force and vertical due to pressure by gravity are equal Commented Aug 12 at 17:04
• @JyothiSrivalli I posted my answer to answer the question as it was back then. However, just immagine for a second that you had some free-standing water column with a weight on top. Just the still picture. What would happen, if time started passing on that arrangement? The weight will fall, the water below it will accelerate downwards together with the weight, and the bottom of the column will splash outwards to make room for the water coming from above. Why? Because there is nothing to hold the pressure of the water laterally, and water will flow to avoid pressure. Commented Aug 12 at 19:52
• The same column within a glass tube, and with a watertight seal between the weight and the glass, and nothing will happen altogether. The water has nowhere to go, the glass withstands the outwards force from the water pressure, and thus, the weight has nowhere to go either. Commented Aug 12 at 19:56

Consider an analogy using the game of snooker. The coloured balls are initially set up in a triangle shape and the white ball is fired at them, When the white ball strikes the coloured balls, they scatter in various directions that are not parallel to the initial motion of the white ball because the normals of the contact points between the balls are not parallel to the initial motion of the white ball. This demonstrates that directions of the forces transferred from molecule to molecule in the liquid are scattered by the random collisions of the molecules in the liquid.

While the molecules of a liquid are not usually exact spheres, the random orientations of the contact normals between the molecules results in vertical forces being redirected in all directions from vertically straight down to completely horizontally. Since pressure is just force divided by the area it acting on, the pressure is exerted in all directions including on vertical faces.

Also imagine a heavy ball dropped onto an plane inclined at 45 degrees. The ball bounces off the inclined plane in a horizontal direction. If the inclined plane is part of a wedge that is free to move horizontally on another surface, them the recoil force will cause the the wedge to accelerate horizontally in the opposite direction to the ball. In this example it is clear that vertical motion is easily changed to horizontal motion and vertical forces are easily redirected to act horizontally. In a fluid at non zero temperature, the molecules are in continuous random vibrational motion relative to each other and this causes molecular motion and forces to be redistributed in all directions.

When I think of a fluid, like water, I think of a material that doesn't resist to shear stresses.

If we think of a vertical surface of water, between two ideally frictionless glass panes, we can study a vertically oriented, small square of water — using a square permits to temporarily confuse stresses and forces.

          | P
v
+----------+
|          |
--->|          |<---
X  |          |  X
|          |
+----------+
^
| P


P is the compressive stress (the pressure), connected to the weight of the water column, and X is an unknown horizontal stress that the OP assumes it's zero (of course no tangential stresses, water is a fluid).

The square is in equilibrium, irrespective of the value of X.

Now consider a different square, rotated by π/4, and consider that the shear forces applied on the sides are equal to zero (water is a fluid) and at the same time must be equal to (P-X)/2, then

(P-X)/2 = 0 ⇒ X = P


Now it's easy to show that, irrespective of the orientation of the square, the compressive stress on each face of the square is always P: the configuration of equilibrium with X = P is invariant with respect to a rotation about the axis perpendicular to the plane.

A slightly different approach

We take into account a small right triangle, with a bottom horizontal side of length b and a vertical side of length h.

On the bottom we have a force σyb, on the side a force σxh and no shear forces because the shear stress (water is a fluid) is zero.

On the upper side, we know that we have no shear force as well, and that

1. The normal force has a vertical component σyb and a horizontal one σxh, for the global equilibrium.
2. Because the normal force must be normal to a line whose projections are b and h, the ratio of the vertical force to the horizontal one must be b/h, so σybxh = b/h ⇒ σx = σy.

Because σyp, the pressure, we have that also σx = p, so we have to show that the normal stress on the other side is also equal to p.

The resultant of the two components is p(b²+h²)1/2, the resultant in terms of σn is σn(b²+h²)1/2, hence also σn = p.

• I am asking that how did the horizontal force come if gravity is in vertical direction Commented Aug 12 at 17:02
• And if I remove both the opposite side forces the water is still in equilibrium Commented Aug 12 at 17:03
• @JyothiSrivalli I won't repeat my answer in a comment. If you had read my answer, the horizontal STRESS comes from the equilibrium of a π/4 rotated "square of water". Why do you ask questions if you're seemingly afraid to change your mind? Commented Aug 12 at 19:22

Like many things in Physics, pressure is a simple concept which is very difficult to adequately explain without the formal definition. This requires differential calculus. I'll spare you the details--in lieu of a textbook, that's wikipedia's job ;).

Unfortunately, you have written two premises that are fundamentally wrong. The first is the statement 'pressure acts in ALL directions'. If you were taught that, it's not that your teacher was mistaken, they were just oversimplifying for the benefit of those who lack your desire for a deeper understanding. So let's throw that statement out and see if we can correct it :).

The second is the role of gravity. Gravity does not play a direct role in the force the water pressure exerts on the object. As you're aware, gravity does play an important indirect role, but that doesn't affect the general answer, so I'll leave it out of this discussion.

It's easier to start thinking about pressure the other way around--from the object's perspective. First, realize that the force exerted by pressure comes from the collective elastic collisions between a vast number of moving molecules of the medium and the outer surface of the object. We have all seen how a ball bounces off a wall or the floor. As others have stated, during the collision the ball's momentum is changed perpendicular to the wall. This is exactly the same situation with all those molecules! Expanding our thinking, we realize that a surface is only able to exert a force on it's enclosing medium in the outward direction. Now, Newton's Third Law says there must be an equal and opposite force, which of course is from the medium on the object. This tells us that the medium is only able to apply an inward force on the surface of the object. This also tells us that pressure exerts a force on any specific bit of the surface in exactly ONE direction (not 'all directions'). Of course, the direction of the force can be different on every bit of the surface, because it depends on the orientation of that exact bit of the surface. The important point is that it is the shape of the object that determines the direction of the force on any part of it's surface. The pressure is simply "in" the medium.

Now we have all the pieces, and we can rewrite your 1st premise in a better form as: "Pressure represents the ability of a medium to exert an inward force on an object that is submerged in it."