Bernoulli's Equation and plugging water hole

AI Thread Summary
To calculate the force on the Dutch boy's finger plugging the hole, the pressure at the depth of the water must be determined using the formula P = ρgh, where ρ is the density, g is the acceleration due to gravity, and h is the depth. The area of the hole can be calculated from its diameter, allowing the force to be found using F = PA. For part b, the time to fill 1 acre of land can be calculated by determining the flow rate through the hole using the previously calculated velocity and the hole's area. The discussion emphasizes the need to apply these fundamental principles of fluid dynamics to solve the problem effectively. Understanding these concepts is crucial for accurately addressing both parts of the homework.
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Homework Statement


Here is the problem, I am able to calculate the velocity, but I don't know where to go from there.

A legendary Dutch boy saved Holland by plugging a hole in a dike with his finger, which is 1.10 cm in diameter.
(a) If the hole was 2.40 m below the surface of the North Sea (density 1030 kg/m3), what was the force on his finger?
(b) If he pulled his finger out of the hole, how long would it take the released water to fill 1 acre of land to a depth of 1 ft assuming the hole remained constant in size? (A typical U.S. family of four uses 1 acre-foot of water, 1234 m3, in 1 year.)

Homework Equations



P1 + (1/2)\rhov12 + \rhogy1 = P2 + (1/2)\rhov22 + \rhogy2

The Attempt at a Solution



I calculated the velocity to be 5.238 m/s, but I have no idea how to get force from this (for part a) or time (part b). Am I missing some other equations?

Thanks
 
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Part a) Hint: You have the diameter of the hole, the depth of the water, and the density of the water. What else do you need to calculate the force on the Dutch Boy's finger? Remember, while the finger is in the hole, velocity = 0.

Part b) Hint: You have the diameter of the hole and the velocity of water flowing through it. You are asked to find out how long it takes a given quantity of water to flow through the hole. What else do you need?
 
I think I got it now, thanks I appreciate it.
 
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