Problem 5. Water at STP flows at a speed of U = 0.20 m/s over a triangular flat plate with a base length of 26 = 1.0 m and angles of e = 45° as shown. (a) Verify that the boundary layer will remain laminar. (b) Integrate wall shear stress over the plate to derive the following relationship for the friction drag on one side of the plate: 0.664 Vtano b? Tu,b, Tw,b = pU². Ub Fp.f Re, Re, (c) Calculate the friction drag for the triangle shown and for a rectangle of width 2b and length b aligned with U. U 26
Problem 5. Water at STP flows at a speed of U = 0.20 m/s over a triangular flat plate with a base length of 26 = 1.0 m and angles of e = 45° as shown. (a) Verify that the boundary layer will remain laminar. (b) Integrate wall shear stress over the plate to derive the following relationship for the friction drag on one side of the plate: 0.664 Vtano b? Tu,b, Tw,b = pU². Ub Fp.f Re, Re, (c) Calculate the friction drag for the triangle shown and for a rectangle of width 2b and length b aligned with U. U 26
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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![**Problem 5.** Water at STP flows at a speed of \( U = 0.20 \, \text{m/s} \) over a triangular flat plate with a base length of \( 2b = 1.0 \, \text{m} \) and angles of \( \theta = 45^\circ \) as shown.
(a) Verify that the boundary layer will remain laminar.
(b) Integrate the wall shear stress over the plate to derive the following relationship for the friction drag on one side of the plate:
\[
F_{D,f} = \frac{8}{3} \sqrt{\tan \theta} \, b^2 \, \tau_{w,b}, \quad \tau_{w,b} = \frac{1}{2} \rho \, U^2 \left(\frac{0.664}{\sqrt{Re_b}}\right), \quad Re_b = \frac{Ub}{\nu}
\]
(c) Calculate the friction drag for the triangle shown and for a rectangle of width \( 2b \) and length \( b \) aligned with \( U \).
**Diagram Explanation:**
The diagram features a triangular flat plate immersed in a fluid with flow velocity \( U \) directed parallel to the base of the triangle. The plate has a base of length \( 2b \) and angles \( \theta = 45^\circ \). The flow is visualized with blue arrows indicating the direction and uniformity of the incoming flow. The triangle’s geometry denotes the span \( 2b \) along the flow direction and its alignment on the coordinate plane defined by \( x, z \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1884fcec-afba-4d7d-98e8-b14c586e79dd%2F84b633a8-2096-4216-83de-dbd639855b72%2Flvq00au_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 5.** Water at STP flows at a speed of \( U = 0.20 \, \text{m/s} \) over a triangular flat plate with a base length of \( 2b = 1.0 \, \text{m} \) and angles of \( \theta = 45^\circ \) as shown.
(a) Verify that the boundary layer will remain laminar.
(b) Integrate the wall shear stress over the plate to derive the following relationship for the friction drag on one side of the plate:
\[
F_{D,f} = \frac{8}{3} \sqrt{\tan \theta} \, b^2 \, \tau_{w,b}, \quad \tau_{w,b} = \frac{1}{2} \rho \, U^2 \left(\frac{0.664}{\sqrt{Re_b}}\right), \quad Re_b = \frac{Ub}{\nu}
\]
(c) Calculate the friction drag for the triangle shown and for a rectangle of width \( 2b \) and length \( b \) aligned with \( U \).
**Diagram Explanation:**
The diagram features a triangular flat plate immersed in a fluid with flow velocity \( U \) directed parallel to the base of the triangle. The plate has a base of length \( 2b \) and angles \( \theta = 45^\circ \). The flow is visualized with blue arrows indicating the direction and uniformity of the incoming flow. The triangle’s geometry denotes the span \( 2b \) along the flow direction and its alignment on the coordinate plane defined by \( x, z \).
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