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Then convert everything to consistent units, for example, BG:. 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. Is this formula dimensionally homogeneous?

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

Is the formula homogeneous? The formula is therefore dimensionally homogeneous and should hold for any unit system. Clearly the formula cannot be dimensionally homogeneous, because B and H do not contain the dimension time.

Convert stress into English units: Using the concepts from Ex.

Arquivos Semelhantes solution manual Frank M. Without peeking into another textbook, find the form of the Galileo number if it contains g in the numerator. What are the dimensions of B? The mass of one molecule of air may be computed as. The proper form of the pipe flow relation is. Now we have reduced the problem to:. What is the only possible dimensionally homogeneous relation for this flow rate?

Set up a differential equation for the ball motion and solve for the instantaneous velocity V t and position z t. Then the formula predict a mean free path of. By comparing with the answer to Prob. Write this formula in dimensional form, using Table White Ana row Enviado por: Can you guess its name? The correct dimensionally homogeneous beam bending formula is thus:. Use these values to estimate the total mass and total number of molecules of air in the entire atmosphere of the earth.

The formula would be invalid for anything except English units ft, sec. In fact, B is not a constant, it hides one of the variables in pipe flow.

Due to element weight, the pressure along the lower and right sides must vary linearly as shown, to a higher value at point C. Amnual group has a customary name, which begins with C.

Clearly, the formula is extremely inconsistent and cannot be used with confidence for any given fluid or condition or units.

Thus the final desired homogeneous relation for dam flow is:. This is quite small. Using Tablewrite this equation in dimensional form:. Is air rarefied at this condition? If not, try to explain the difficulty and how it might be converted to a more homogeneous form. The relation is now.

Find the maximum height zmax reached by the ball and compare your results with the elementary-physics solktion of zero air drag. This equation, soluion all theoretical partial differential equations in mechanics, is dimensionally homogeneous.

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

Therefore the Stokes- Oseen formula derived in fact from a theory is dimensionally homogeneous. For homogeneity, the right hand side must have dimensions of stress, that is. White – 5th edition solution manual Frank M. Thus hydrostatic pressures cannot keep mdchanics element in balance, and shear and flow result. 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.

The parameter B must have dimensions of inverse length. Convert this water usage into a gallons per minute; and b liters per second. Vertical forces are presumably in balance with element weight included. The formula is dimensionally homogeneous and can be used solutipn any system of units. Substitute flkid given data into the proposed formula:.

Test each term in sequence:. 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. This acceleration is negative, as expected, and reaches a minimum near point B, which is found by differentiating the acceleration with respect to x:.