Are the fields described in Problems 1.11 and 1.12 dimensionally homogeneous? What must th...

Are the fields described in Problems 1.11 and 1.12 dimensionally homogeneous? What must the units of ρ∞ be in order that the pressure be in pounds per square foot when v∞ is given in feet per second (Problem 1.11)?

Problems 1.11

Find the pressure gradient at point (a,b) when the pressure field is given by

where ρ∞, v∞, a, and b are constants.

Problems 1.12

Find the temperature gradient at point (a, b) at time t = (L2/α) ln e when the temperature field is given by

where T0, α, a, and b are constants.