Calculating Fluid Force on Circular Plate in Water Tank

In summary, we have a circular plate in a tank filled with water and we are trying to find the fluid force on it using the given equation and measurements in feet. By splitting the equation and using a trig substitution, we can solve for the integral and find the fluid force.
  • #1
kari82
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Find the fluid force on the circular plate shown in figure (see attachment). Assume the plates are in the wall of a tank filled with water and the measurements are given in feet.

F=w∫h(y)L(y) dy

I have that h(y)= 7-y and L(y)=2√(4-y^2). Therefore, F=2(62.4)∫(7-y)√(4-y^2) dy from y=0 to y=4. Can someone please help me find the integrate of this equation. Thanks!
 

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  • #2
hi kari82! :smile:

(try using the X2 icon just above the Reply box :wink:)
kari82 said:
… Therefore, F=2(62.4)∫(7-y)√(4-y^2) dy from y=0 to y=4. Can someone please help me find the integrate of this equation. Thanks!

you have ∫ (7 - y)√(4 - y2) dy, so just split it up …

∫ 7√(4 - y2) dy can be solved by a trig substitution, and

∫ y√(4 - y2) dy is obvious! :wink:
 

FAQ: Calculating Fluid Force on Circular Plate in Water Tank

How do you calculate the fluid force on a circular plate in a water tank?

The fluid force on a circular plate in a water tank can be calculated by multiplying the density of the fluid, the acceleration due to gravity, and the area of the plate. This equation is known as the buoyancy force formula and is represented as F = ρ * g * A, where ρ is the density of the fluid, g is the acceleration due to gravity, and A is the area of the plate.

What is the significance of calculating fluid force on a circular plate in a water tank?

Calculating the fluid force on a circular plate in a water tank is important in many engineering and scientific applications. It helps in determining the stability and strength of structures, such as dams and bridges, that are submerged in water. It also plays a key role in designing efficient and safe underwater vehicles and equipment.

Can the shape of the plate affect the fluid force calculation?

Yes, the shape of the plate can affect the fluid force calculation. The buoyancy force formula assumes that the plate is completely submerged in the fluid, and the force is evenly distributed over the entire surface area. If the plate has a different shape, such as a cone or a sphere, the calculation will differ based on the shape and the orientation in the fluid.

How does the depth of the water in the tank impact the fluid force calculation?

The depth of the water in the tank does not directly affect the fluid force calculation. However, it does affect the pressure at different depths, which in turn can affect the buoyancy force calculation. This is because the pressure at the bottom of the tank is greater than the pressure at the top, resulting in a larger fluid force at the bottom of the plate.

Are there any limitations to the fluid force calculation on a circular plate in a water tank?

Yes, there are some limitations to the fluid force calculation on a circular plate in a water tank. The calculation assumes that the fluid is incompressible, the plate is completely submerged, and there are no external forces acting on the plate. Additionally, it does not take into account factors such as water velocity, turbulence, and surface tension, which can affect the fluid force in real-life scenarios.

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