Pressure in Fluids: Why Does It Act in All Directions?

[Mårten]

I've read (and experienced!) that pressure in fluids acts in all directions. Why is it so? I understand that if you dive 5 meters down in the water, the water's weight is greater than 1 meter below water surface. So if I'm standing up there under the water, I should feel a greater pressure on the top of my head. But why also on the side of my head?

 

[Dadface]

Because the water molecules are bashing into you from all directions.

 

[jamesb-uk]

The large amount of water above you would be inflicting pressure on all of the water molecules below it, so these molecules are under even more pressure, and would 'want' to relieve that pressure by spreading out away from other molecules, just as if you squash a sponge, it spreads out and gets wider.

I'm not sure whether I've explained that well enough.

 

[ltjlogic]

Pressure is an interesting topic. It is defined as a normal force force exerted by a fluid per unit area. If you were to draw a free body diagram for the object under consideration, you would have 4 normal forces perpendicular to your object (let's say a box). Thus, you would have an arrow going in on the left, bottom, right, and top, along with the weight of the object. You might know from physics that if an object exerts a force, that means there is an equal but opposite force also present. Pressure in a fluid increases with depth because more fluid "rests" on deeper layers, and the effect of this "extra weight" on a deeper layer is balanced by an increase in pressure. If you were calculating the pressure at a given point 10 meters below the surface of water, you would have to take P(atm) + \rhogz, \rho being the density of water, and taking g to be 9.81 m/s^{}2. It's interesting to note that moving left and right in the water does not cause a pressure change.

I hope this helped answer your question a little bit!

 

[dE_logics]

Water is fluid, i.e even though the pressure of g comes from the top, it gets distributed cause of the fluid nature (and so the tendency to attain even pressure density).

 

[ltjlogic]

I don't know if you can just say, "it gets distributed cause of the fluid nature." Of course it gets distributed because of its fluid nature. Also, I don't know what you mean by "even though the pressure of g comes from the top." When looking at pressure you have to understand that it is the normal force exerted by the fluid per unit area. You have to take into consideration the gravity involved at that point, along with the mass times the gravity of the object you're looking at -- perhaps a person underwater.

 

[tiny-tim]

pressure is isotropic because …

I've read (and experienced!) that pressure in fluids acts in all directions. Why is it so? I understand that if you dive 5 meters down in the water, the water's weight is greater than 1 meter below water surface. So if I'm standing up there under the water, I should feel a greater pressure on the top of my head. But why also on the side of my head?

Hi Mårten!

Imagine your head is triangular, with the top and back of your head horizontal and vertical, respectively, and your face sloping backwards at an angle θ.

If the pressures on your top back and face, and their areas, are p_T p_B and p_F, and A_T A_B and A_F, and if your head is in equilibrium (and ignoring gravity), then since pressure is normal to the surface, p_FcosθA_F = p_BA_B, and p_FsinθA_F = p_TA_T.

But, from geometry, cosθA_F = A_B, and sinθA_F = A_T.

So p_F = p_B = p_T.

 

[Mårten]

Thanks folks, that helped me a lot! I'm well on my way to understand this better now. I liked the sponge metaphor.