To determine the height of the fluid above the ground, we can apply the principles of fluid mechanics, specifically Torricelli's law. Torricelli's law states that the speed of efflux through a hole in a tank is related to the height of the fluid above the hole.
The equation representing Torricelli's law is as follows:
v = √(2gh)
Where:
- v is the speed of efflux (9.8 m/s in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s²)
- h is the height of the fluid above the hole (what we need to find)
Rearranging the equation to solve for h:
h = (v²) / (2g)
Substituting the given values:
h = (9.8 m/s)² / (2 * 9.8 m/s²)
Simplifying the equation:
h = 4.9 m²/s² / 9.8 m/s²
h = 0.5 m
Therefore, the height of the fluid above the ground is 0.5 meters.