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Test each term in sequence:. Vertical forces are presumably in balance with element weight included. From Table A-2, its viscosity is 1. If not, try to explain the difficulty and how it might be converted to a more homogeneous form. 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. In fact, B is not a constant, it hides one of the variables in pipe flow.

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

The proper form of the mechaanics flow relation is. The formula is dimensionally homogeneous and can be used with any system of units. This acceleration is negative, as expected, and reaches a minimum near point B, which is found by differentiating the acceleration with respect to x:. Use these values to estimate the total mass and total number of molecules of air in the entire atmosphere of the earth. Is this formula dimensionally homogeneous?


If M is proportional to L, find its form. The formula admits to an arbitrary dimensionless constant C whose value can only be obtained from known data.

Therefore the Stokes- Oseen formula derived in fact from a theory is dimensionally homogeneous. Clearly, the formula is extremely inconsistent and cannot be used with flhid for any given fluid or condition or units. Arquivos Semelhantes solution manual Frank M.

Can this equation be used with confidence for a variety of liquids and gases? Can you guess its name? Thus the final desired homogeneous relation for dam flow is:.

This equation, like all theoretical partial differential equations in mechanics, is dimensionally homogeneous.

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

This is quite small. By comparing with the answer to Prob. Then convert everything to consistent units, for example, BG:. Clearly the formula cannot be dimensionally homogeneous, because B and H do not contain the dimension time. Write this formula in dimensional form, using Table White – 5th edition solution manual Frank M. The correct dimensionally homogeneous beam bending formula is thus:. Set up a differential equation for the ball motion and solve for the instantaneous velocity V t and position z t.


The formula would be invalid for anything except English units ft, sec. What are the dimensions of B? The mechancs B must have dimensions of inverse length. This group has a customary name, which begins with C. Due to element weight, the pressure along the lower and right sides must vary linearly as shown, to a higher value at point C.

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

The relation is now. Is the formula homogeneous? What is the only possible dimensionally homogeneous relation for this flow rate? The mass of one molecule of air may be computed as.

Substitute the given data into the proposed flhid.

The formula is therefore dimensionally homogeneous and should hold for any unit system. For homogeneity, 4rh right hand side must have dimensions of stress, that is. Now we have reduced the problem to:. Find the maximum height zmax reached by the ball and compare your results with the elementary-physics case of zero air drag.