Answered: ted by the simple linear expression, u…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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$**10-97** The streamwise velocity component of a steady, incompressible, laminar, flat plate boundary layer of boundary layer thickness $ \delta $ is approximated by the simple linear expression, $ u = Uy/\delta $ for $ y < \delta $, and $ u = U $ for $ y > \delta $ (Fig. P10–97). Generate expressions for displacement thickness and momentum thickness as functions of $ \delta $, based on this linear approximation. Compare the approximate values of $ \delta^*/\delta $ and $ \theta/\delta $ to the values of $ \delta^*/\delta $ and $ \theta/\delta $ obtained from the Blasius solution. **Answers:** 0.500, 0.167 The diagram accompanying this question shows a flat plate with a boundary layer depicted. The flow velocity $ U $ is indicated as constant outside the boundary layer, and a velocity profile within the boundary layer is represented by a triangular gradient from zero at the plate to $ U $ at the boundary thickness $ \delta $. Vectors indicate the direction and relative velocity of the flow across the boundary layer. *(10-97 provided as context for 10-98 only)*$

Transcribed Image Text:**10-97** The streamwise velocity component of a steady, incompressible, laminar, flat plate boundary layer of boundary layer thickness $ \delta $ is approximated by the simple linear expression, $ u = Uy/\delta $ for $ y < \delta $, and $ u = U $ for $ y > \delta $ (Fig. P10–97). Generate expressions for displacement thickness and momentum thickness as functions of $ \delta $, based on this linear approximation. Compare the approximate values of $ \delta^*/\delta $ and $ \theta/\delta $ to the values of $ \delta^*/\delta $ and $ \theta/\delta $ obtained from the Blasius solution. **Answers:** 0.500, 0.167 The diagram accompanying this question shows a flat plate with a boundary layer depicted. The flow velocity $ U $ is indicated as constant outside the boundary layer, and a velocity profile within the boundary layer is represented by a triangular gradient from zero at the plate to $ U $ at the boundary thickness $ \delta $. Vectors indicate the direction and relative velocity of the flow across the boundary layer. *(10-97 provided as context for 10-98 only)*

**Problem 5:**

**10–103** Air at 30°C flows at a uniform speed of 30.0 m/s along a smooth flat plate. Calculate the approximate x-location along the plate where the boundary layer begins the transition process toward turbulence. At approximately what x-location along the plate is the boundary layer likely to be fully turbulent?
**Answers:** 5 to 6 cm, 1 to 2 m

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