At what speed does water escape from a large open-top tank through an opening 2.00 cm in diameter. The opening is 3.00 m below the water level of the tank on the side of the tank.
To determine the speed at which water escapes from a large open-top tank, you can use Torricelli's law of efflux, also known as Torricelli's theorem. This law states that the speed of efflux (v) is given by the equation:
v = √(2gh)
Where:
- v is the speed of efflux (in meters per second)
- g is the acceleration due to gravity (approximately 9.8 m/s²)
- h is the vertical height difference between the water level in the tank and the opening (in meters)
In this case, the height difference (h) is given as 3.00 m, so we can substitute this value into the equation:
v = √(2 * 9.8 * 3.00)
Calculating this:
v = √(58.8)
v ≈ 7.67 m/s
Therefore, the water will escape from the tank through the 2.00 cm diameter opening at a speed of approximately 7.67 meters per second.