?Which of the following equations below are dimensionally homogeneous? a) To = T

Question

?Which of the following equations below are dimensionally homogeneous?

a) To = T + (pV)^2T^2/2cpp/R^2 where T is temperature, p is density, V is velocity, cp is the heat capacity, p is pressure, and R is the gas constant for a particular gas. b) CL = L/0.5pU^2A, where CL is a dimensionless lift coefficient, L is the lift force, p is the density, U is the velocity, and A is the area. c) Q = k/n AR^1/3 h S0^1/2, where Q is the discharge, k is a dimensionless coefficient, n is a coefficient with units of s/m^1/3, A is area, Rh is a radius, and S0 is the sine of an angle.

Explanation / Answer

A and C are dimensionally homogeneous

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