Calculate position of plate between two fluids

In summary, the conversation discusses a problem involving a plate and two fluids with different shear stresses. The goal is to find the thickness of the plate. The attempt at a solution involves equating the shear stresses and using a substitution to find the answer. However, it is noted that the problem may not be fully specified.
  • #1
bill222
1
0

Homework Statement


Problem is as shown in the picture.
djA3Hjh.png

The answer is meant to be a 4.59mm.

Homework Equations


Tau=mu(du/dy)

The Attempt at a Solution


Force (tau) acting on plate from both fluids is equal, as is velocity (du).

mu1 (du/dy1) = mu2 (du/dy2)

mu1/dy1 = mu2/dy2
(mu2/mu1) *y1 = y2

y1 + y2 + plate thickness = width
y1 + y2 + 0.7937 = 12.7 mm

By substituting in mu2/mu1 *y1 = y2 I obtain the answer y1 = 3.31 mm.Any help is much appreciated
 
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  • #2
Who says that the force (or shear stress) exerted by each fluid on the plate has to be the same? It seems to me this problem is under-specified.
 

1. How do you calculate the position of a plate between two fluids?

The position of a plate between two fluids can be calculated using the following formula: y = (ρ1d1 + ρ2d2) / (ρ1 + ρ2), where y is the position of the plate, ρ1 and ρ2 are the densities of the two fluids, and d1 and d2 are the distances of the plate from the top of each fluid.

2. What factors affect the position of a plate between two fluids?

The position of a plate between two fluids is affected by the densities and depths of the two fluids, as well as the shape and weight of the plate. The viscosity and temperature of the fluids may also play a role in the positioning.

3. Can the position of a plate between two fluids be calculated for any shape of plate?

Yes, the formula for calculating the position of a plate between two fluids is applicable for any shape of plate, as long as the plate is submerged in both fluids and its weight is evenly distributed.

4. How do you account for irregularities in the fluids when calculating the position of a plate?

To account for irregularities in the fluids, the density and depth of the fluids can be divided into smaller sections and the position of the plate can be calculated for each section. The overall position of the plate can then be determined by taking the average of these individual positions.

5. Is there a more accurate method for calculating the position of a plate between two fluids?

Yes, there are more complex methods such as using computational fluid dynamics (CFD) simulations that take into account the flow patterns and turbulence of the fluids. However, for simple cases, the aforementioned formula is accurate enough for practical applications.

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