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The correct dimensionally homogeneous beam bending formula is thus:. Therefore the Stokes- Oseen formula derived in fact from a theory is dimensionally homogeneous.

If not, try to explain the difficulty and how it might be converted to a more homogeneous form. Set up a differential equation for the ball motion and solve for the instantaneous velocity V t feank position z t. Can you guess its name?

### Solution Manual – Fluid Mechanics 4th Edition – Frank M. White

The formula is therefore dimensionally homogeneous and should hold for any unit system. The formula admits to an arbitrary dimensionless constant C whose value can only be obtained from known data.

For homogeneity, the right hand side must have dimensions of stress, that is. Without peeking into another textbook, find the form of the Galileo number if it contains g in the numerator.

Write this formula in dimensional form, using Table If M is proportional to L, find its form. Then the formula predict a mean free path of.

The parameter B must have dimensions of inverse length. Find the maximum height zmax reached by the ball and compare your results with the elementary-physics case of zero air drag. What is the only possible dimensionally fdition relation for this flow rate?

### Solution Manual – Fluid Mechanics 4th Edition – Frank M. White | Benoit Dozois –

Thus hydrostatic pressures cannot editino the element in balance, and shear and flow result. The formula is dimensionally homogeneous and can be used with any system of units. This group has a customary name, which begins with C. Then convert everything to consistent units, for example, BG:. Use these values to estimate the total mass and total number of molecules of air in the entire atmosphere of the earth.

Now we have reduced the problem to:. Vertical forces are presumably in balance with element weight included. This equation, like all theoretical partial differential equations in mechanics, is dimensionally homogeneous. Substitute the given data into the proposed formula:. This whiet quite small.

Clearly the formula cannot be dimensionally homogeneous, because B and H do not contain the dimension time. Test each term in sequence:. Using the concepts from Ex. The formula would be invalid for anything except English units ft, sec. This acceleration is negative, as expected, and reaches a minimum near point B, which is found by differentiating the acceleration with respect to x:. In fact, B is not a constant, it hides one of the variables in pipe flow.

Clearly, the formula is extremely inconsistent and cannot be used with confidence for any given fluid or condition or units. Convert stress into English units: By comparing with the answer to Prob. Arquivos Semelhantes solution manual Frank M.

White – 5th mechanice solution manual Frank M. Due to element weight, the pressure along the lower and right sides must vary linearly as shown, to a higher value at point C. From Table A-2, its viscosity is 1. Is air rarefied at this condition? 4yh

## Solution Manual – Fluid Mechanics 4th Edition – Frank M. White

Thus the final desired homogeneous relation for dam flow is:. White Ana row Enviado por: Convert this water usage into a gallons per minute; and b liters per second. What are the dimensions of B? The relation is now. The mass of one molecule of air may be computed as. Actually, the Hazen-Williams formula, still in common use in the watersupply industry, is valid only for water flow in smooth pipes larger than 2-in.

The proper form of the pipe flow relation is. Can this equation be used with confidence for a variety of liquids and gases?

Is this formula dimensionally homogeneous? Is the formula homogeneous? Using Tablewrite this equation in dimensional form:. But horizontal forces are out of balance, with the unbalanced force being to the left, due to the shaded excess-pressure triangle on the right side BC.