whit38220_ch07

# whit38220_ch07 - Chapter 7 Flow Past Immersed Bodies 7.1...

This preview shows pages 1–3. Sign up to view the full content.

Chapter 7 Flow Past Immersed Bodies 7.1 For flow at 20 m/s past a thin flat plate, estimate the distances x from the leading edge at which the boundary layer thickness will be either 1 mm or 10 cm, for (a) air; and (b) water at 20 ° C and 1 atm. Solution: (a) For air, take ρ = 1.2 kg/m 3 and µ = 1.8E 5 kg/m s. Guess laminar flow: 22 1/2 5.0 (0.001) (1.2)(20) ,: ( 1 ) 25 25(1.8 5) laminar x U or x Ans. air mm xE Re δδ == = = 0.0533 m 1.2(20)(0.0533)/1.8 5 71,000 , x Check Re E OK laminar flow =− = (a) For the thicker boundary layer, guess turbulent flow: 1/7 0.16 ( a 1 0 ) (/ ) turb solve for Ans. cm x Ux δ ρµ = x6 . 0 6m = 8.1 6, , x Check Re E OK turbulent flow = (b) For water, take = 998 kg/m 3 and = 0.001 kg/m s. Both cases are probably turbulent: = 1 mm: x turb = 0.0442 m , Re x = 882,000 (barely turbulent) Ans. ( water—1 mm ) = 10 cm: x turb = 9.5 m , Re x = 1.9E8 (OK, turbulent) Ans. ( water—10 cm ) 7.2 Air, equivalent to a Standard Altitude of 4000 m, flows at 450 mi/h past a wing which has a thickness of 18 cm, a chord length of 1.5 m, and a wingspan of 12 m. What is the appropriate value of the Reynolds number for correlating the lift and drag of this wing? Explain your selection. Solution: Convert 450 mi/h = 201 m/s, at 4000 m, = 0.819 kg/m s, T = 262 K, = 1.66E 5 kg/m s. The appropriate length is the chord , C = 1.5 m, and the best parameter to correlate with lift and drag is Re C = (0.819)(201)(1.5)/1.66E 5 = 1.5E7 Ans. 7.3 Equation (7.1 b ) assumes that the boundary layer on the plate is turbulent from the leading edge onward. Devise a scheme for determining the boundary-layer thickness more accurately when the flow is laminar up to a point Re x ,crit and turbulent thereafter. Apply this scheme to computation of the boundary-layer thickness at x = 1.5 m in 40 m/s

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
476 Solutions Manual Fluid Mechanics, Fifth Edition flow of air at 20 ° C and 1 atm past a flat plate. Compare your result with Eq. (7.1 b ). Assume Re x ,crit 1.2E6. Fig. P7.3 Solution: Given the transition point x crit , Re crit , calculate the laminar boundary layer thick- ness δ c at that point, as shown above, c /x c 5.0/Re crit 1/2 . Then find the “apparent” distance upstream, L c , which gives the same turbulent boundary layer thickness, c 1/7 cc L /L 0.16/Re . Then begin x effective at this “apparent origin” and calculate the remainder of the turbulent boundary layer as /x eff 0.16/Re eff 1/7 . Illustrate with a numerical example as requested. For air at 20 ° C, take ρ = 1.2 kg/m 3 and µ = 1.8E 5 kg/m s. c crit c c 1/2 1/6 7/6 c c 1.2(40)x 5.0(0.45) Re 1.2E6 if x 0.45 m, then 0.00205 m 1.8E 5 (1.2E6) U 0.00205 1.2(40) Compute L 0.0731 m 0.16 0.16 1.8E 5 == = = ±² ³ ´ µ¶ µ ·¸ ¹º » ¼ Finally, at x = 1.5 m, compute the effective distance and the effective Reynolds number: eff c c eff eff 1.5 m eff 1.2(40)(1.123) x x L x 1.5 0.0731 0.45 1.123 m, Re 2.995E6 1.8E 5 0.16x 0.16(1.123) Re (2.995E6) Ans. =+ − = + = = ≈= | 0.0213 m Compare with a straight all-turbulent-flow calculation from Eq. (7.1 b ): x1 . 5 m 1.2(40)(1.5) 0.16(1.5) Re 4.0E6, whence (25% higher) .
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/30/2008 for the course MAE 3400 taught by Professor Bryan during the Winter '05 term at Missouri (Mizzou).

### Page1 / 87

whit38220_ch07 - Chapter 7 Flow Past Immersed Bodies 7.1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online