Suppose there is a small hole (radius=0.0203) at the base of a large tank. If the height of water in the tank is 15m (a) what is the speed of water escaping through the hole? (b) Calculate the amount of water (in cubic meters per second) escaping the tank.

To determine the speed of water escaping through the hole, you can use Torricelli's law. Torricelli's law states that the speed of a fluid coming out of a small hole at the bottom of a container is given by the equation:

v = sqrt(2 * g * h)

where:
- v is the speed of water escaping through the hole
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height of the water column above the hole

(a) Now, we can substitute the given values into the equation:

v = sqrt(2 * 9.8 * 15)

Let's calculate the speed using this equation:

v = sqrt(294) ≈ 17.15 m/s

Therefore, the speed of water escaping through the hole is approximately 17.15 m/s.

(b) To calculate the amount of water escaping per second, we need to find the flow rate. The flow rate is given by the equation:

Q = A * v

where:
- Q is the flow rate (in cubic meters per second)
- A is the cross-sectional area of the hole
- v is the speed of water escaping through the hole

The cross-sectional area of the hole can be calculated using the formula:

A = π * r^2

where:
- A is the cross-sectional area
- r is the radius of the hole

Given that the radius of the hole is 0.0203 m, we can calculate the cross-sectional area:

A = π * (0.0203)^2

Let's calculate the cross-sectional area using this equation:

A ≈ 0.0012973 m^2

Now, we can calculate the amount of water escaping per second using the flow rate equation:

Q = 0.0012973 * 17.15 ≈ 0.0222 m^3/s

Therefore, the amount of water escaping the tank per second is approximately 0.0222 cubic meters.