Hydrostatic pressure on triangular plate

In summary, the problem involves finding the hydrostatic force against one side of a submerged triangle with given dimensions. The solution involves using the equation \int_{a}^{b}{\rho}g(x)w(x)dx and similar triangles to find the appropriate values for a, w, and the force.
  • #1
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Homework Statement



A triangle with base 3 m and height 4 m is submerged vertically in water so that the tip is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it.

Homework Equations



[tex]
\int_{a}^{b}{\rho}g(x)w(x)dx
[/tex]

The Attempt at a Solution



I keep getting the wrong answer. Does it look like I'm setting it up right?

Using similar triangles

I have [tex]a = \frac{3}{4\sqrt{2}}\left(4-xi^{*}\right)[/tex]

[tex]wi^{*}=2\left(\frac{\sqrt{3}}{2}-a\right)[/tex]

[tex]a\mbox{re}a=wi\; \Delta x=\left( \sqrt{3}\; -\; 3\frac{\sqrt{2}}{2}+\frac{3}{4\sqrt{2}}x \right)[/tex]

Pressure = 1000gx

Force = P*A
 

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  • #2
No. I'm not sure where you're getting the sqrt(3)/2 from in your formulas for a and w. Also, why not use similar triangles to find w directly as a function of x instead of going through the mess with a?
 
  • #3
a=3/8(4-xi)

Sorry, I don't know where I got that either. I must need some rest.
 
  • #4
Area=3/4xi(delta x)

Does this look right?
 
  • #5
Looks good.
 
  • #6
Got it. Thank you for your help.
 

1. What is hydrostatic pressure on a triangular plate?

Hydrostatic pressure on a triangular plate is the force exerted by a static fluid on a triangular-shaped plate, per unit area. It is caused by the weight of the fluid above the plate and is dependent on the depth and density of the fluid.

2. How is hydrostatic pressure calculated on a triangular plate?

The formula for calculating hydrostatic pressure on a triangular plate is P = γh, where P is the pressure, γ is the specific weight of the fluid, and h is the depth of the fluid above the plate.

3. What is the difference between hydrostatic pressure and hydrodynamic pressure?

Hydrostatic pressure is the force exerted by a static fluid on a surface, while hydrodynamic pressure is the force exerted by a moving fluid on a surface. Hydrodynamic pressure is caused by the velocity of the fluid and is dependent on factors such as flow rate and fluid viscosity.

4. How does the shape of a triangular plate affect hydrostatic pressure?

The shape of a triangular plate does not significantly affect hydrostatic pressure, as long as the plate is submerged in the same fluid at the same depth. However, the surface area of the plate will affect the total force exerted by the fluid on the plate.

5. What are some real-world applications of hydrostatic pressure on triangular plates?

Some examples of real-world applications of hydrostatic pressure on triangular plates include calculating the force on a submerged dam or retaining wall, determining the stability of a submerged object under water, and understanding the pressure distribution on the surface of an airplane wing in flight.

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