Bernoulli's Equation and plugging water hole

In summary, the conversation discusses a physics problem involving a legendary Dutch boy who saved Holland by plugging a hole in a dike with his finger. The problem asks for the force on his finger and the time it takes for a given quantity of water to flow through the hole. The conversation provides hints and equations to help solve the problem.
  • #1
KKuff
9
0

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)[itex]\rho[/itex]v12 + [itex]\rho[/itex]gy1 = P2 + (1/2)[itex]\rho[/itex]v22 + [itex]\rho[/itex]gy2

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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  • #2
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?
 
  • #3
I think I got it now, thanks I appreciate it.
 

Related to Bernoulli's Equation and plugging water hole

1. What is Bernoulli's Equation?

Bernoulli's equation is a fundamental equation in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a moving fluid. It states that as the velocity of a fluid increases, the pressure decreases, and vice versa.

2. How is Bernoulli's Equation applied to plugging a water hole?

In the context of plugging a water hole, Bernoulli's equation can be used to determine the amount of force required to prevent water from flowing out of the hole. By increasing the velocity of the water entering the hole, the pressure at the hole decreases, making it easier to plug with a smaller force.

3. Can Bernoulli's Equation be used for both liquids and gases?

Yes, Bernoulli's equation can be applied to both liquids and gases, as long as the flow is steady, the fluid is incompressible, and there is no friction present. However, for gases, additional considerations such as compressibility and temperature changes may need to be taken into account.

4. What are some real-world applications of Bernoulli's Equation?

Bernoulli's equation has numerous applications in engineering and physics, including aerodynamics, hydraulics, and ventilation systems. It is also used in everyday objects such as carburetors, airplane wings, and showerheads.

5. Can Bernoulli's Equation be used to explain the lift force on an airplane wing?

Yes, Bernoulli's equation is commonly used to explain the lift force on an airplane wing. As air flows over the curved shape of the wing, it must travel a longer distance compared to the air flowing under the wing. This results in a difference in velocity and pressure, creating an upward force on the wing.

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