physics question about pressure

Question

1. What are the total force and the absolute pressure on the bottom of a swimming pool 22.0 m by 8.50 m whose uniform depth is 2.00 m?
2. What will be the pressure against the side of the pool near the bottom?

Answer 1

Step 1 Draw a picture

(A simple Swimming pool with 22x8.5x2 dimensions)

Step 2 List all information

L= 22.0 m

W= 8.5 m

D= Δh = 2 m

ρ= density of water = 1x10³kg/m³

g= 9.8 m/sec²

P = total pressure= ?

F = total force= ?

P_o= 1.013 x 10⁵N/m²

Step 3 Use the Formula and substitute P = Po + (p •g •Δh)

P = Po + (p •g •Δh)

P = (1.013 x 10⁵N/m²) + [1x10³kg/m³][9.8 m/sec²][2 m]

P = (1.013 x 10⁵N/m²) + [1.96 x10⁴N/m²]

P = (1.013 x 10⁵N/m²) + [0.196 x10⁵N/m²]

P = (1.209 x 10⁵N/m²) Total Pressure

STEP 4

So we have the pressure now we can get the force...

F = P ⋅A

F = (1.209 x 10⁵N/m²)(22.0 m)(8.5 m)

F = 2.26 x 10⁷N/m^2. Total Force

b) Pressure is same in all directions at a given depth- REMEMBER AT A GIVEN DEPTH THE PRESSURE IS THE SAME IN ALL DIRECTIONS

Answer 2

The specific weight of water is 9.807 kN/m³

b) the pressure at the bottom of the pool is 9.807 kN/m³ x 2 m = 19.614 kN/m² but this is the gage pressure, find the absolute pressure by adding 1 atmosphere of pressure = 101.353 kN/m²

a) Force at the bottom = F = PA = 19.614 kN/m² x (22 x 8.5)m² = 3,667.82 kN