Air at T = 30degreeC and P = 1 atm flows through a smooth circular duct of diame

Question

Air at T = 30degreeC and P = 1 atm flows through a smooth circular duct of diameter D = 1 cm at a volumetric flowrate of Q = 2.356 * 10-4 m3/s. We wish to learn the following aspects of this scenario. Determine the flow state (laminar or tubulent?). Calculate the entry region, l/D. Integrate a suitable velocity profile to find an expression for the volumetric flowrate. From this relation, determine the centerline velocity, Vc. Rework part (a) for water at the same temperature. Comment on any differences you notice. (Hint: Use an exact velocity profile if possible. If an exact solution does not exist, an approximate/empirical profile may be necessary.)

Explanation / Answer

a) Velocity V = Q/A = (2.356*10^-4)/(3.14/4*0.01^2) = 3 m/s

Re = Vd/ = 3*0.01/(15.68*10^-6) = 1914

Since Re<2300, flow is laminar.

For laminar flow, Entry region l/D = 0.06*Re = 0.06*1914 = 114.8

Assume, u/Vc = 1 - (r/R)^2

Q = [Integral (2r) u dr]0R = 2Vc [Integral (r - r^3/R^2) dr]0R = 2Vc [r^2/2 - r^4/(4R^2)]0R = 1/2*VcR^2

Vc = 2Q/(R^2) = 2*(2.356*10^-4)/(*(0.01/2)^2) = 6 m/s

b) For water, Re = Vd/ = 3*0.01/(0.801*10^-6) = 37453

Since Re>2300, flow is turbulent.

For turbulent flow, entry region l/D = 4.4*Re^(1/6) = 4.4*37453^(1/6) = 25.45

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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