The gage pressure in a liquid at a depth of 3 m is read to be 50 kpa. determine the gage pressure in the same liquid at a depth of 9 m.

The Gauge pressure at 9 meters depth is

Explanation:

Gauge pressure is the difference between absolute pressure and some reference pressure, most commonly atmospheric pressure. The increment in pressure caused by a static fluid is given by:

where is the density of the liquid,  g is the accleration due to gravity and d is the depth.

Now, we see that is linearly proportional to d, and we can assume that remains constant, because liquids are usually not compressible.

Given that the greater depth is simply 3 times the smaller depth:

at of depth will also be three times the gauge pressure at of depth.

We could also have calculated ny using:

and used this result to calculate the gauge pressure. These are both similar methods that yield the same result