Fluid ?ow dynamics are characterized by dimensionless numbers describing the rat

Question

Fluid ?ow dynamics are characterized by dimensionless numbers describing the ratio of forces on the ?uid. One such number characterizes the ratio of inertia to the force of surface tension: W=(pv^2l)/o Where W is dimensionless, p is the mass density of the ?uid, v is the speed of the ?uid, and l is a characteristic length scale of the ?uid. For this equation to be dimensionally correct, what are the dimensions of surface tension o? A. Setup [representative drawing(s), de?nition and categorization of quantities]: B. What variable(s) from the setup are you looking for? C. Solve for the quantities in Part B in terms of the known quantities you

Explanation / Answer

P = MASS DENSITY = M/V = [M][L]^-3 V = VELOCITY = [L][T]^-1 SO THE DIMENSIONS OF SURFACE TENSION ARE = [M][L]^-3 * {[L][T]^-1}^2 *[L] = [M][T]^-2

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