The mean free path of a gas (let\'s call it l) is the average distance traveled

Question

The mean free path of a gas (let's call it l) is the average distance traveled by gas molecules between collisions with each other. A simplified correlation for ideal gases is l = 1.26mu / rho root RT. where mu is the viscosity of the gas.rho is its density. T is its temperature, and R is the ideal gas constant. Write the dimensions (not units!) of the above correlation, and show that the equation is dimensionally homogeneous. Note that the constant 1.26 is a dimensionless constant - it has no dimensions or units. Estimate the mean free path of air at T = 20.0 degree C and P = 0.100 atm. The flow of a gas around an object is considered rarified when the mean free path of the gas is on the same order of magnitude as (or larger than) the length scale of the object under analysis. When the flow is rarefied, the equations of fluid flow require special treatment beyond the scope of this course (we call this rarefied gas dynamics), because the fluid can no longer be treated as a continuum. Consider flow of air over a 1.0 mm diameter object under the conditions of part (b). Is it necessary to use rarefied gas flow theory? Why or why not? Discuss. Namely, for what size objects is rarefied gas theory required under these conditions?

Explanation / Answer

RHS=[kg/(s m)]/[kg/m^3 * K^1/2 * K^-1/2 * kg*m/s] =m LHS=m hence roved

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.