A small hole is cut in the bottom of a water storage tank. The depth of the water is 8.00 m. If the diameter of the small hole in the bottom of the tank is 1.00 cm, then what is the flow rate of the water leaving the tank? A) 9.83 × 10⁻⁴ m³/s B) 8.75 × 10⁻⁴ m³/s C) 8.21 × 10⁻⁴ m³/s D) 7.45 × 10⁻⁴ m³/s E) 7.21 × 10⁻⁴ m³/s

Question

Quizplus · Accepted Answer

The flow rate of water leaving the tank can be calculated using Bernoulli's equation, which relates the velocity of fluid flow to the pressure and depth of the fluid.

The equation for flow rate is: 
Q = A * v 
where Q is flow rate, A is the area of the hole, and v is the velocity of the water leaving the hole.

To find the velocity, we can rearrange Bernoulli's equation: 
v = sqrt(2gh) 
where g is the acceleration due to gravity, and h is the depth of the water in the tank.

Plugging in the given values: 
g = 9.81 m/s^2 
h = 8.00 m

Using the diameter of the hole, we can calculate the area: 
A = pi*r^2 
r = 0.500 cm = 0.00500 m 
A = pi*(0.00500 m)^2 = 7.85*10^-8 m^2

Now we can calculate the flow rate: 
Q = A * v = (7.85*10^-8 m^2) * sqrt(2*9.81 m/s^2 * 8.00 m)

Q = 9.83*10^-4 m^3/s = 9.83*10^-4 L/s

Converting to mL/s: 
Q = 9.83*10^-1 mL/s = 9.83*10^2 uL/s

Therefore, the best choice is A, with a flow rate of 9.83×10−4 m^3/s.

A Small Hole Is Cut in the Bottom of a Water