The velocity field in the region shown is given by V = ( aj + byk ) where a = 10 m/s and b = 5 s-1. For the 1 m x 1 m triangular control volume (depth w = 1 m perpendicular to the diagram), an element of area 1 may be represented by dÁ1 = wdzj– wdyk and an element of area ( by dA2 = = -wdyk. Z. Control volume y P4.4 a. Find an expression for V · dA1. b. Evaluate SA, V • dA1. c. Find an expression for V · dA2. d. Find an expression for V(V. dA2 e. Evaluate Sa, V(V. dA,).-
The velocity field in the region shown is given by V = ( aj + byk ) where a = 10 m/s and b = 5 s-1. For the 1 m x 1 m triangular control volume (depth w = 1 m perpendicular to the diagram), an element of area 1 may be represented by dÁ1 = wdzj– wdyk and an element of area ( by dA2 = = -wdyk. Z. Control volume y P4.4 a. Find an expression for V · dA1. b. Evaluate SA, V • dA1. c. Find an expression for V · dA2. d. Find an expression for V(V. dA2 e. Evaluate Sa, V(V. dA,).-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The velocity field in the region shown is given by V =
vỹ = (
aj + byk ) where a = 10 m/s and b = 5 s-1. For the 1 m × 1 m triangular control volume
(depth w = 1 m perpendicular to the diagram), an element of area (1 may be represented by dA1 = wdzj– wdyk and an element of area (2 by dA2 = -wdyk.
Z.
2
Control
volume
→ y
P4.4
a. Find an expression for V · dA1.
b. Evaluate Sa, V. dA1.
c. Find an expression for V · dA2.
d. Find an expression for V (v. dAz).
e. Evaluate
· dA2
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