Measured along the surface of the water, a rectangular swimming pool has a length of 15.9 m. Along this length, the flat bottom of the pool slopes downward at an angle of 16.9 ° below the horizontal, from one end to the other. By how much does the pressure at the bottom of the deep end exceed the pressure at the bottom of the shallow end?

Question

Measured along the surface of the water, a rectangular swimming pool has a length of 15.9 m. Along this length, the flat bottom of the pool slopes downward at an angle of 16.9 ° below the horizontal, from one end to the other. By how much does the pressure at the bottom of the deep end exceed the pressure at the bottom of the shallow end?

Answer 1

The difference in height is 15.9sin16.9

pressure difference=density*heightdifference*9.8N/kg

density needs to be in kg/m^3

Answer 2

by .483kg/sq.cm

Answer 3

tan16.9 = h/15.9, h = .3038x15.9 = 4.831m

P=w.h 1000kg/cu.m x 4.831m x 9.81=4831N/sq.m

Answer 4

To answer this question, we need to understand the concept of hydrostatic pressure and how it varies with depth.

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. In this case, the fluid is water in the swimming pool. The pressure at a given depth in a fluid depends on the density of the fluid, the acceleration due to gravity, and the depth from the surface.

Let's break down the problem into a few steps to calculate the pressure difference between the deep end and the shallow end.

Step 1: Find the difference in depth between the deep and shallow end.
Given that the flat bottom of the pool slopes downward at an angle of 16.9°, we can use trigonometry to find the difference in depth.

depth difference = length of the pool x sin(angle)
depth difference = 15.9 m x sin(16.9°)

Step 2: Calculate the pressure difference using the hydrostatic pressure formula.
The hydrostatic pressure at a certain depth can be calculated using the formula:

pressure = density of the fluid x acceleration due to gravity x depth

To find the pressure difference, we can subtract the pressure at the shallow end from the pressure at the deep end.

pressure difference = pressure at the deep end - pressure at the shallow end

Note: The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s².

Let's calculate the pressure difference:

pressure difference = (density of water x acceleration due to gravity x depth difference)

Substituting the values we found earlier:

pressure difference = 1000 kg/m³ x 9.8 m/s² x (depth difference)

Now, you can substitute the value of the depth difference we calculated in Step 1 to find the pressure difference.