Final answer:
To find the flow rate of water emerging from the hole in the container, we can use the principle of continuity and Bernoulli's equation. The flow rate can be calculated by finding the speed of the water at the hole using Bernoulli's equation and multiplying it by the area of the hole.
Step-by-step explanation:
The flow rate of water emerging from the hole in the container can be determined using the principle of continuity. The principle states that the product of the area of the hole and the speed of the water is constant. To find the flow rate, we need to find the speed of the water. We can use Bernoulli's equation, which relates the speed of the water to the pressure difference between the top surface of the water and the hole.
Given that the hole has an area of 10 cm² and is located 5 m below the surface of the water, we can calculate the pressure difference using the formula:
P2 - P1 = ρgh
Where P2 is the atmospheric pressure at the top surface of the water, P1 is the pressure at the hole, ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the hole.
Once we have the pressure difference, we can use Bernoulli's equation to find the speed of the water at the hole. The equation is:
v1 = sqrt(2(P2 - P1) / ρ)
Finally, we can calculate the flow rate using the formula:
Q = A*v1