Bernoulli's Equation and plugging water hole

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SUMMARY

The discussion revolves around applying Bernoulli's Equation to solve a physics problem involving fluid dynamics. The problem presents a scenario where a hole in a dike is plugged, and the user calculates the water velocity at 5.238 m/s. To find the force on the finger plugging the hole, the user needs to utilize the hole's diameter (1.10 cm) and the water's density (1030 kg/m³) along with the depth of the water (2.40 m). For part b, the user must determine the time it takes for the released water to fill 1 acre of land to a depth of 1 ft, using the calculated velocity and the hole's dimensions.

PREREQUISITES
  • Understanding of Bernoulli's Equation
  • Knowledge of fluid density and pressure concepts
  • Basic skills in calculating area and volume
  • Familiarity with units of measurement in physics
NEXT STEPS
  • Calculate the force exerted by the water on the finger using the formula: Force = Pressure × Area.
  • Determine the time taken for water to flow through the hole using the formula: Time = Volume / Flow Rate.
  • Explore the implications of fluid dynamics in real-world applications, such as dike management.
  • Review additional fluid mechanics principles, such as continuity equation and flow rate calculations.
USEFUL FOR

Students studying physics, particularly those focusing on fluid dynamics, engineers involved in hydraulic systems, and anyone interested in practical applications of Bernoulli's Equation.

KKuff
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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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