Total force and pressure

Question

a) Determine the total force and the absolute pressure on the bottom of a
swimming pool 25.0 meters by 9.5 meters, whose uniform water depth is 2.0
meters.

 

b) what will be the pressure against the side of the pool near the bottom?

Answer 1

Hi Meg,

 

This might be a trick question in three parts.  

 

Part I:  Total pressure due to water column above a 1 m² area on the floor of the pool is P = ρgh = (1000 kg/m³)×(9.8 m/s²)×(2 m) = 19,600 N/m² .  The surface area of the pool is A = (25 m) (9.5 m) = 237.5 m².  The force on the bottom of the pool due to the water F = P A = 4.66x10⁶ N.

 

Part II:   Atmospheric pressure also "presses" on the surface of the pool with a force of F = (101,325 N/m²)x(237.5 m2) = 24.0x10⁶ N.  Thus the total force could be either 4.66 MN or 28.7 MN  (rounding significant figures a little bit, and where MN = 10⁶ N) and the "absolute" pressure could be  either 19,600 N/m² (as in Part I) or 120,925 N/m² (as in Part II - depending on your text's context).  

 

Part III:  Pressure in any direction  (i.e. on the wall) very near the bottom will be nearly the same as at the bottom.  Therefore the answer(s) in Part II will be the same for (b).

 

[Comment:  you could argue that the net force on the pool is zero, since the pool is not moving,  but I would doubt that this is what was meant by "the total force" in (a) above -  context is important and English is imprecise]