Calculating Force on a Tank Hatch in Water

In summary, the problem involves determining the force exerted by water on a tank hatch that is hinged at the top and has dimensions of 1.15 m by 1.90 m. The given equation for the force, F, is incorrect and should be replaced with Wρg[H1(H1/2-H2/3)]. This is due to the nature of integrals and the need to use the average pressure on the hatch rather than the pressure at a specific point.
  • #1
VelvetRebel
16
0
Force of a Tank Hatch in terms of Pressure

Homework Statement



The tank shown in the figure below is filled with water to a depth of H1 = 1.88 m.
http://educog.com/res/brookscole/serway/Physics_for_Scientists_and_Engineers_6ed/Chap14/graphics/serb1514.gif
At the bottom of one of the side walls is a rectangular hatch H2 = 1.15 m high and W = 1.90 m wide. The hatch is hinged at its top. Determine the magnitude of the force that the water exerts on the hatch.

Homework Equations


F=[tex]\int^{H1-H2}_{0} W\rho g(H1-y)dy[/tex]

The Attempt at a Solution


The equation above is what my professor gave us in class to use for this problem.
For the solved integral, I got:
W[tex]\rho[/tex]g[H1y-y2/2]
After putting in all the numbers, I don't get the right answer. Is my solved integral wrong? Or did my professor give us the wrong integral?
 
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  • #2
Before you do the maths, think about the answer.
Specifically think about what a integral means in this case.

(hint - 'average' pressure on the hatch?)
 
  • #3


EDIT: Nevermind, I figured it out.
 
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1. What is the purpose of a tank hatch?

The tank hatch is used to provide access to the inside of the tank for maintenance, inspection, and filling or emptying of the tank.

2. How does the pressure of a tank hatch affect the tank?

The pressure of a tank hatch can affect the overall pressure inside the tank, as well as the stability and structural integrity of the tank itself. If the pressure inside the tank is too high, it can cause the hatch to become difficult to open or close, or even result in damage to the hatch or tank.

3. What factors contribute to the pressure of a tank hatch?

The pressure of a tank hatch is influenced by several factors, including the type of material the tank is made of, the size and shape of the hatch, the contents and level of the tank, and any external forces such as temperature or pressure changes.

4. How can the pressure of a tank hatch be controlled?

The pressure of a tank hatch can be controlled by adjusting the pressure inside the tank, ensuring proper ventilation and air flow, and regularly maintaining the hatch to ensure it is functioning properly.

5. What safety precautions should be taken when dealing with the pressure of a tank hatch?

When dealing with the pressure of a tank hatch, it is important to follow all safety procedures, wear appropriate protective gear, and properly maintain and inspect the hatch and tank. If the pressure becomes too high, it is important to release it in a controlled manner to prevent accidents or damage.

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