Calculate Speed of Efflux of Water

What is the speed of efflux of water from the hole?

Can you determine the volume discharged per unit time?

Speed of Efflux of Water

The speed of efflux of water from the hole is approximately 17.6 m/s.

Volume Discharged Per Unit Time

The volume discharged per unit time is approximately 0.186 m^3/s.

To calculate the speed of efflux of water from the hole, we can use Torricelli's law. According to Torricelli's law, the velocity of fluid flowing from an opening is equal to the square root of twice the acceleration due to gravity multiplied by the height difference between the opening and the surface of the fluid.

In this case, the height difference is the depth of the tank, which is 14.0 m. Assuming the tank is open to the atmosphere, the pressure inside the tank is approximately atmospheric pressure. By using the formula v = sqrt(2 * g * h), where g is the acceleration due to gravity (approximately 9.8 m/s^2), we can calculate the speed of efflux to be approximately 17.6 m/s.

For determining the volume discharged per unit time, we need to find the cross-sectional area of the hole. Since the hole is circular, we can calculate its area using A = π * r^2, where r is the radius of the hole (half of the diameter). With the radius being half of 6.00 mm (0.003 m), we can then calculate the volume discharged per unit time using the formula Q = A * v, where Q is the volume flow rate, A is the area of the hole, and v is the speed of efflux. By substituting the values, we get Q = (π * (0.003)^2) * 17.6, simplifying to 0.186 m^3/s.