Fluid Mechanicsa) The hydrostatic equation is: (p/gamma)+z=C, where p is pressure, gamma is specific weight, and C is a constant. Show that this equation is dimensionally homogeneous.b) Would a check for dimensionless homogenity have saved the Mars Climate Orbiter? Why or why not?

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Asked Aug 24, 2019
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Fluid Mechanics

a) The hydrostatic equation is: (p/gamma)+z=C, where p is pressure, gamma is specific weight, and C is a constant. Show that this equation is dimensionally homogeneous.

b) Would a check for dimensionless homogenity have saved the Mars Climate Orbiter? Why or why not?

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Expert Answer

Step 1

The hydrostatic equation is given, and it is to be shown that it is dimensionally homogeneous. This can be done as,

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P z C, where, P is pressure, y is the specific weight, z is the elevation and C Y is a constant Now, let us write the dimensions of P, y, and z M P LT M Y12T z L

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Step 2

Substituting all the respective dimensions in the equation, we get,

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L272 L C M LT L L C

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Step 3

Now since on the LHS of the equation, we have a dimension of length for both  and Z. Therefore, the c...

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