A large water tank is 18m above the ground. Suppose a pipe with a diameter of 8cm is connected to the tank and leads down to the ground. How fast does the water rush of the piper at ground level? Assume that the tank is open to the atmosphere.

To determine the speed at which water rushes out of the pipe at ground level, we can apply Torricelli's law, which states that the velocity of a fluid flowing out of a small opening is given by the formula:

v = √(2gh)

where:
v is the velocity of the fluid (water in this case),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
h is the height difference between the water level in the tank and the pipe opening.

In this case, the height difference (h) is the distance from the water level in the tank to the ground level. Given that the tank is 18m above the ground, the height difference is 18m.

Now, let's substitute these values into the formula:

v = √(2 * 9.8 * 18)

Simplifying,

v = √(352.8)

v ≈ 18.77 m/s

Therefore, the water rushes out of the pipe at ground level at a speed of approximately 18.77 m/s.