Pressure gauge submerged in a fluid column

[TyErd]

Homework Statement

What reading will we see on a pressure gauge that is at the middle and bottom of a fluid column? and why

Homework Equations

P=pgh where p is density and P is pressure

The Attempt at a Solution

Well according to the equations as the gauge drop lower and lower it should decrease in pressure meaning before the gauge is dropped in it must have a greater than zero reading on the gauge and as it descends it reduces until it reaches zero, however that cannot be the case because pressure will increase when an object is submerged under water. Does it have something to do with buoyancy?

 

[SteamKing]

Try again Ty. The pressure is greater at the bottom of a fluid column. h is measured from the free surface of the fluid

 

[TyErd]

so that means the readings will be opposite? so the gauge pressure at the top will be zero since h is zero?

 

[fleem]

so that means the readings will be opposite? so the gauge pressure at the top will be zero since h is zero?

The equation gives the pressure at the bottom of a column, given the columns height. To use this equation, we simply define the gauge position as the bottom of the column. (We know that the fluid below the gauge does not affect its reading).

 

[rwisz]

Yes, you are correct. The reading on the pressure gauge will increase as it descends to the bottom of the fluid column. This is because the pressure at any given depth in a fluid is directly proportional to the density of the fluid and the depth of the fluid above it. As the gauge descends, the depth of the fluid above it increases, resulting in an increase in pressure. This is also known as hydrostatic pressure.

In addition, buoyancy can also play a role in the reading on the pressure gauge. If the gauge is not fully submerged in the fluid, the buoyant force acting on it will decrease the effective weight of the gauge and therefore decrease the pressure reading. However, if the gauge is fully submerged, the buoyant force will be negligible and the pressure reading will only depend on the depth of the fluid column.

Overall, the reading on the pressure gauge at the middle and bottom of the fluid column will be higher than the reading at the top, due to the increase in depth and density of the fluid.