FluidMechWhite5eCh07 - Chapter 7 Flow Past Immersed Bodies...

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

View Full Document Right Arrow Icon
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
Background image of page 1

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

View Full DocumentRight Arrow Icon
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) .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 87

FluidMechWhite5eCh07 - Chapter 7 Flow Past Immersed Bodies...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online