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

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.

For homogeneity, the right hand side must have dimensions of stress, that is. Test each term in sequence:. Actually, the Hazen-Williams formula, still in common use in the watersupply industry, is valid only for water flow in smooth pipes solutiion than 2-in. Find the maximum height zmax reached by the ball and compare your results with the elementary-physics case of zero air drag.

Without peeking into another textbook, find the form of the Galileo number if it contains g in the numerator. The formula is dimensionally homogeneous and can be used with any system of units. The mass of one molecule of air may be computed as. Set solutipn a differential equation for the ball motion and solve for the instantaneous velocity V t and position z t.


The proper form of the pipe flow relation is. By comparing with the answer to Prob.

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

Arquivos Semelhantes solution manual Frank M. Thus hydrostatic pressures cannot keep the element in balance, and shear and flow sooution. Is this formula dimensionally homogeneous? This equation, like all theoretical partial differential equations in mechanics, is dimensionally homogeneous. This group has a customary name, which begins with C. Using Tablewrite this equation in dimensional form:.

This is quite small.

Due to element weight, the pressure along the lower and right sides must vary linearly as shown, to a higher value at point C. The formula admits to an arbitrary dimensionless constant C whose value can only be obtained from known data.

Then the formula solutioon a mean free path of. Therefore the Stokes- Oseen formula derived in fact from a theory is dimensionally homogeneous.

In fact, B is not a constant, it hides one of the variables in pipe flow. Using the concepts from Ex. White – 5th edition solution manual Frank M. Write this formula in dimensional form, using Table The relation is now. Clearly, the formula is extremely inconsistent and cannot be used with confidence for any given fluid or condition or units. Convert this water usage into a gallons per minute; and b liters per second. Can you guess its name?


The formula would be invalid for anything except English units ft, sec. Now we have reduced the problem to:. From Table A-2, its viscosity is 1.

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

What is the only possible dimensionally homogeneous relation for this flow rate? Is air rarefied at this condition?

This acceleration is negative, as expected, and reaches a minimum near point B, which is found by differentiating the acceleration with respect to x:. Convert stress into English units: Use these values to estimate the total mass and total number of molecules of air in the entire atmosphere of the earth. The correct dimensionally homogeneous beam bending formula is thus:.