Flow rate problem (boat in water, with pic?)

In summary, to find the volume of water that has accumulated in the boat after one hour, we can use Bernoulli's equation to calculate the velocity of the water flowing into the boat through the hole. We can then use the continuity equation to equate the flow rate at the surface of the water (point 1) with the flow rate at the hole (point 2) and solve for the velocity at point 2. This will allow us to calculate the volume of water that has entered the boat.
  • #1
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Homework Statement


A yacht sitting in a harbor has a hole (area 8x10-3) in its hold and is located 2 meters below the surface of the water. The interior of the boat is at atmospheric pressure. If the hole went unnoticed for one hour, how much water has accumulated in the boat?

Here's my crappy attempt at an image
[PLAIN]http://img197.imageshack.us/img197/3097/yachtf.jpg [Broken]

Homework Equations


Bernoulli's Equation
Flow=Area*Speed


The Attempt at a Solution


No clue. I ended up finding the difference is pressure between the air and water pressure at 2 meters and got a huge negative number. I know it involves Bernoulli's equation but how do we find the speed of the water flowing in? The equation has P1 + .5pv12 and P2 + .5pv22. What's the difference between those? Pressures are different but isn't the speed of the water the same flowing in on both sides of the equation?
 
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  • #2




Thank you for your question. It seems like you're on the right track by using Bernoulli's equation to solve this problem. However, there are a few key pieces of information that you will need to consider in order to find the speed of the water flowing in through the hole.

First, let's review Bernoulli's equation: P1 + ½ρv1^2 + ρgh1 = P2 + ½ρv2^2 + ρgh2. This equation describes the conservation of energy for a fluid moving through a pipe or other system. P represents pressure, ρ represents density, v represents velocity, and h represents height. The numbers 1 and 2 refer to two different points in the system, and the equation states that the total energy at point 1 (pressure energy + kinetic energy + potential energy) is equal to the total energy at point 2.

In this problem, we can assume that the water is initially at rest at the surface of the harbor (point 1) and is flowing into the boat through the hole (point 2). The pressure at point 1 is equal to atmospheric pressure, and the height at point 1 is 0 meters since the surface of the water is our reference point. The pressure at point 2 is equal to the pressure inside the boat, which is also atmospheric pressure. However, the height at point 2 is 2 meters since the hole is located at this depth.

Now, we need to find the velocity at point 2 in order to solve for the volume of water that has entered the boat. To do this, we can use the continuity equation, which states that the flow rate (volume per time) at any point in a system is equal to the product of the cross-sectional area and the velocity at that point (Q = A * v). In this case, the flow rate at point 2 is equal to the flow rate at point 1, since the water is not being compressed or expanding as it flows through the hole. Therefore, we can set the flow rate at point 2 equal to the flow rate at point 1 and solve for the velocity at point 2.

I hope this helps you to solve the problem and understand the concepts involved. Good luck!
 

What is a flow rate problem involving a boat in water?

A flow rate problem involving a boat in water is a mathematical problem that involves calculating the speed of a boat relative to the water and the speed of the water itself.

How is the flow rate of a boat in water calculated?

The flow rate of a boat in water is calculated by using the equation: flow rate = boat speed + water speed. This equation takes into account the relative speeds of the boat and the water to determine the overall flow rate.

What factors can affect the flow rate of a boat in water?

Some factors that can affect the flow rate of a boat in water include the size and shape of the boat, the shape and depth of the water, and any external forces such as wind or currents. These factors can impact the speed and direction of the boat, as well as the speed of the water.

How can I solve a flow rate problem involving a boat in water?

To solve a flow rate problem involving a boat in water, you will need to know the relative speeds of the boat and the water, as well as any other relevant information such as distance or time. You can then use the flow rate equation to calculate the overall flow rate.

Why are flow rate problems involving a boat in water important?

Flow rate problems involving a boat in water are important because they can help us understand the dynamics of objects moving through fluids. They also have practical applications, such as in navigation and marine engineering, where the speed and direction of a boat in relation to the water are crucial factors to consider.

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