A swimming pool measures 10m by 7m by 2m calculate the full force exerted by the water against the bottom. What is the pressure at the bottom due to the water?
water is about 1000 kg/m^3
we have 140 m^3 of water
so 140,000 kg of water
the force of gravity on that is
9.81 * 140,000 = 1,373,400
Newton's third law says the bottom of the pool has to push up with that same force 1,373,400 Newtons
pressure = force/area
= 1,373,400/(10*7) = 19,620 Newtons/m^2 or Pascals
By the way, that is pressure above atmospheric or "gage" pressure. For absolute pressure you need to add one atmosphere to that or about 100,000 Pascals. This is not normally done because the atmosphere also pushes up from underneath.
To calculate the force exerted by the water against the bottom of the pool, we need to multiply the pressure exerted by the water by the area of the bottom surface.
First, let's calculate the pressure at the bottom of the pool due to the water:
Pressure is defined as force divided by area (P = F/A). In this case, the force is the weight of the water and the area is the surface area of the bottom of the pool.
To calculate the weight of the water, we use the formula:
Weight = mass * gravity
The mass of the water can be calculated using the density and volume of the water:
Mass = density * volume
In this case, the density of water is approximately 1000 kg/m³ and the volume is the length times the width times the depth of the pool.
Volume = length * width * depth
Once we have the mass of the water, we can calculate the weight using the acceleration due to gravity, which is approximately 9.8 m/s².
Now, let's calculate the force exerted by the water against the bottom:
Force = Weight
Finally, to find the pressure at the bottom, we divide the force by the area of the bottom surface, which is the length times the width of the pool:
Pressure = Force / (length * width)
By substituting the given dimensions into the equations and performing the above calculations, you'll be able to find the full force exerted by the water against the bottom of the pool and the pressure at the bottom due to the water.