How is fluid pressure related to fluid depth

It depends on the fluid.

For (approximately) incompressible fluids, the pressure is (approximately) linearly related to the depth.


For compressible fluids, it will depend on the curve of pressure vs. density.

See answer below

Step-by-step explanation:

In this case, we can assume that this function follows a linear function. In this case, the general expression would be:

y = a + bx

Where:

a: Y intercept

b: slope of the function

To get the slope we need to apply the following expression:

b = y₂ - y₁ / x₂ - x₁

We already have two points, (80,0) and (40,16) from here, we can determine the slope:

b = 16 - 0 / 40 - 80

b = -16/40

b = -2/5

Now that we know the slope, we can determine the y-intercept if it have:

a = y - bx

Using any point, we can calculate it:

a = 0 - (-2/5*80)

a = 0 + 160/5

a = 32

With these two values, we can write the function:

h(x) = 32 - 2/5x

Hope it helps