5.42. Derive Eq. 6.29. It is suggested that you use the coordinates shown in Fig. 6.27. Here the flow is in the x direction from left to right, and the slit extends a distance / in the z direction and / >> h. Choose as your element for the force balance a piece symmetrical about the y axis (other choices are possible but lead to more difficult mathematics). Hint: This is a repeat of the derivation of Eq. 6.8 in a different geometry. Simply follow that derivation, changing the geometry. y=-1/2- y=-=h y=0 · Δι FIGURE 6.27 Suggested dimensions for Prob. 6.42.

International Edition---engineering Mechanics: Statics, 4th Edition
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Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.30P
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Consider how the new geometry in this problem affects the math/boundary condition/derivation. Both equations are listed!

6.42. Derive Eq. 6.29. It is suggested that you use the coordinates
shown in Fig. 6.27. Here the flow is in the x direction from left
to right, and the slit extends a distance / in the z direction and /
>> h. Choose as your element for the force balance a piece
symmetrical about the y axis (other choices are possible but
lead to more difficult mathematics). Hint: This is a repeat of the
derivation of Eq. 6.8 in a different geometry. Simply follow that
derivation, changing the geometry.
y=1/12
y==h
y=0
FIGURE 6.27
Suggested dimensions for Prob. 6.42.
Transcribed Image Text:6.42. Derive Eq. 6.29. It is suggested that you use the coordinates shown in Fig. 6.27. Here the flow is in the x direction from left to right, and the slit extends a distance / in the z direction and / >> h. Choose as your element for the force balance a piece symmetrical about the y axis (other choices are possible but lead to more difficult mathematics). Hint: This is a repeat of the derivation of Eq. 6.8 in a different geometry. Simply follow that derivation, changing the geometry. y=1/12 y==h y=0 FIGURE 6.27 Suggested dimensions for Prob. 6.42.
V=
P₁
- (ΡΑΕ)
Q=
rá - r2 P – P2
4μ
Δε
(6.29)
(6.8)
Transcribed Image Text:V= P₁ - (ΡΑΕ) Q= rá - r2 P – P2 4μ Δε (6.29) (6.8)
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