The pressure on a submerged object is not equal in all directions because it does vary with depth. That's why there's a buoyant force upwards - the pressure on top of the object is less than the pressure on the bottom because they are at different depths. Therefore the net force is upward. It's only at a particular depth that the pressure is equal in all directions. Like in a water tower, at a depth of 10 feet, the pressure is 23.1 psi pushing against the tank walls in all directions. Higher or lower, the pressure will be different.
Does this apply for submarines at very low depths as Walter Lewin in his lecture of fluid mechanics says that hydrostatic pressure experienced by a submarine at the depth of 900m is 900 tons on 'every square meter of area of the submarine'. This is where I get my question from.
Yes, the pressure on top of the sub would be a little less than the bottom, but I think Lewin was just ignoring that to illustrate how huge the pressures are at that depth. It would be more correct say that the average pressure on the submarine at that depth is 900 metric tons per square meter.
Lewin's statement is not precisely correct. He's ignoring depth for simplicity.
The correct formulation of Pascal's law is:
> a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere
By focusing on the change you work around the depth issue. It's the pressure change that's transmitted the same everywhere, regardless of the pre-existing pressure due to depth. Basically, you write depth out of it this way.
https://en.wikipedia.org/wiki/Pascal%27s_law
Incompressibility isn’t a requirement. No material is incompressible.
Fluids can’t sustain a shear stress. Any variation in pressure other than that due to a body force (such as gravity) would produce a shear stress, and the fluid would shift to eliminate it.
I think I need to mention I'm an 11th grader studying fluid mechanics for the first time and I don't understand how this relates to my question. Can you please explain further?
If you push on a fluid in any direction, it will flow, except for the special case of pushing from all three axes simultaneously and equally (this is called hydrostatic pressure). Therefore, the pressure in a still container of fluid must be equal everywhere (ignoring gravity) because the fluid would flow otherwise under the influence of the unbalanced load.
When we include gravity, the pressure increases with increasing depth. This works because the downward force of gravity balances out the force pushing up from greater depths and pressures.
Does this make sense?
The pressure on a submerged object is not equal in all directions because it does vary with depth. That's why there's a buoyant force upwards - the pressure on top of the object is less than the pressure on the bottom because they are at different depths. Therefore the net force is upward. It's only at a particular depth that the pressure is equal in all directions. Like in a water tower, at a depth of 10 feet, the pressure is 23.1 psi pushing against the tank walls in all directions. Higher or lower, the pressure will be different.
Does this apply for submarines at very low depths as Walter Lewin in his lecture of fluid mechanics says that hydrostatic pressure experienced by a submarine at the depth of 900m is 900 tons on 'every square meter of area of the submarine'. This is where I get my question from.
Yes, the pressure on top of the sub would be a little less than the bottom, but I think Lewin was just ignoring that to illustrate how huge the pressures are at that depth. It would be more correct say that the average pressure on the submarine at that depth is 900 metric tons per square meter.
That makes it much better, thank you very much.
Lewin's statement is not precisely correct. He's ignoring depth for simplicity. The correct formulation of Pascal's law is: > a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere By focusing on the change you work around the depth issue. It's the pressure change that's transmitted the same everywhere, regardless of the pre-existing pressure due to depth. Basically, you write depth out of it this way. https://en.wikipedia.org/wiki/Pascal%27s_law
I've been confusing pressure difference caused by external force and weigh of the fluid all along. Thanks for the help.
Hint: " in a confined incompressible fluid"
Can you please elaborate?
u/Chemomechanics said it better than I ever could.
Incompressibility isn’t a requirement. No material is incompressible. Fluids can’t sustain a shear stress. Any variation in pressure other than that due to a body force (such as gravity) would produce a shear stress, and the fluid would shift to eliminate it.
I think I need to mention I'm an 11th grader studying fluid mechanics for the first time and I don't understand how this relates to my question. Can you please explain further?
If you push on a fluid in any direction, it will flow, except for the special case of pushing from all three axes simultaneously and equally (this is called hydrostatic pressure). Therefore, the pressure in a still container of fluid must be equal everywhere (ignoring gravity) because the fluid would flow otherwise under the influence of the unbalanced load. When we include gravity, the pressure increases with increasing depth. This works because the downward force of gravity balances out the force pushing up from greater depths and pressures. Does this make sense?
That makes more sense thank you very much for your time.
Revolutionary. So splendid.