# Hydrostatic Fluid- Linearly Accelerating Slope

• AnnaJa
In summary, the angle α of the slope can be calculated using the equation α = γ - θ, where γ is the angle between the slope and the original horizontal plane, and θ is the angle between the water surface and the original horizontal plane. Substituting the values given, we get α = 3.54°.
AnnaJa

## Homework Statement

An open rectangular tank contains water up to about half of its depth. This tank accelerates at a=2.20 m/s$^{2}$ up a slope α (alpha), which causes the free water surface to form an angle θ (theta) with the original horizontal plane.
What is the α angle of the slope?

## Homework Equations

p=ρh(g$\stackrel{+}{-}$a)
tanθ=$\stackrel{a}{g}$

## The Attempt at a Solution

θ=tan$^{-1}($$\stackrel{199}{1242}$)=9.1°

angle between water surface and slope = γ

γ= α+θ

tanγ=($\stackrel{a}{g}$)

tanγ=($\stackrel{2.2}{9.81}$)

γ=12.64°

α=γ-θ=12.64-9.1=3.54°

I am not sure if this is the right approach?

Any help would be greatly appreciated.
Thank you, Anna

#### Attachments

• Hyd Accel.png
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Hello Anna,

Firstly, great job on using the appropriate equations and attempting to solve the problem. Your approach is mostly correct, but there are a few things that can be improved upon.

1. The angle θ that you calculated is incorrect. To find the angle between the water surface and the original horizontal plane, we need to use the inverse tangent function with the ratio of the opposite side (199) to the adjacent side (1242). So, θ = tan^-1(199/1242) = 9.1°.

2. The angle γ that you calculated is also incorrect. The angle between the slope and the original horizontal plane is not the same as the angle between the water surface and the slope. To find this angle, we can use the inverse tangent function with the ratio of the opposite side (a) to the adjacent side (g). So, γ = tan^-1(a/g) = tan^-1(2.2/9.81) = 12.64°.

3. Now, to find the angle α, we need to use the fact that the angle θ is formed by the slope and the original horizontal plane, and the angle γ is formed by the water surface and the slope. So, we can use the following equation: γ = α + θ. Substituting the values, we get α = γ - θ = 12.64° - 9.1° = 3.54°.

So, your final answer is correct! Good job. Just make sure to double check your calculations and try to understand the problem and the equations better. Keep up the good work!

## 1. What is a hydrostatic fluid?

A hydrostatic fluid is a liquid that is at rest and under the influence of gravity. This means that the fluid is not moving and the only forces acting on it are due to its weight and the pressure exerted by the surrounding environment.

## 2. How does a hydrostatic fluid behave on a linearly accelerating slope?

On a linearly accelerating slope, the hydrostatic fluid will remain at rest and the pressure at any given point will be proportional to the depth and density of the fluid at that point. The fluid will also experience a pseudo force due to the acceleration of the slope, but this will not affect its behavior.

## 3. What factors affect the behavior of a hydrostatic fluid on a linearly accelerating slope?

The behavior of a hydrostatic fluid on a linearly accelerating slope is primarily affected by the slope angle, acceleration of the slope, and the density and depth of the fluid. Other factors such as viscosity and surface tension may also play a role, but to a lesser extent.

## 4. Can a hydrostatic fluid move on a linearly accelerating slope?

No, a hydrostatic fluid will not move on a linearly accelerating slope as long as the slope is not steep enough to overcome the pressure forces of the fluid. However, if the slope angle becomes too steep, the fluid may start to flow or even spill over the edge of the slope.

## 5. How is the pressure of a hydrostatic fluid calculated on a linearly accelerating slope?

The pressure of a hydrostatic fluid on a linearly accelerating slope can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid from the surface. This formula applies as long as the fluid is at rest and the slope is not too steep.

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