HW6 - University of Iowauser.engineering.uiowa.edu/~me_160/2019/HW Solutions/HW6.pdfP3.150 In Prob....

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HW6

Transcript of HW6 - University of Iowauser.engineering.uiowa.edu/~me_160/2019/HW Solutions/HW6.pdfP3.150 In Prob....

Page 1: HW6 - University of Iowauser.engineering.uiowa.edu/~me_160/2019/HW Solutions/HW6.pdfP3.150 In Prob. 3.60 find the torque caused around flange 1 if the center pomt of exit 2 is 1.2

HW6

Page 2: HW6 - University of Iowauser.engineering.uiowa.edu/~me_160/2019/HW Solutions/HW6.pdfP3.150 In Prob. 3.60 find the torque caused around flange 1 if the center pomt of exit 2 is 1.2
Page 3: HW6 - University of Iowauser.engineering.uiowa.edu/~me_160/2019/HW Solutions/HW6.pdfP3.150 In Prob. 3.60 find the torque caused around flange 1 if the center pomt of exit 2 is 1.2

steady

ρdw

dt= ρg + μ

d2w

dx2

ρg + μd2w

dx2= 0,

d2w

dx2= −

𝜌𝑔

𝜇

dw

dx= −

𝜌𝑔

𝜇𝑥 + 𝐶1, w(x) = −

𝜌𝑔

2𝜇𝑥2 + 𝐶1𝑥 + 𝐶2

Boundary condition 𝑤(−ℎ) = 0 → w(−h) = 0 = −𝜌𝑔

2𝜇ℎ2 − 𝐶1ℎ + 𝐶2

𝑤(ℎ) = 0 → w(h) = 0 = −𝜌𝑔

2𝜇ℎ2 + 𝐶1ℎ + 𝐶2

∴ 𝐶1 = 0 , 𝐶2 =𝜌𝑔

2𝜇ℎ2

▶ w(x) = −𝜌𝑔

2𝜇𝑥2 +

𝜌𝑔

2𝜇ℎ2

w(x) =𝜌𝑔

2𝜇(ℎ2 − 𝑥2) Ans.

Page 4: HW6 - University of Iowauser.engineering.uiowa.edu/~me_160/2019/HW Solutions/HW6.pdfP3.150 In Prob. 3.60 find the torque caused around flange 1 if the center pomt of exit 2 is 1.2
Page 5: HW6 - University of Iowauser.engineering.uiowa.edu/~me_160/2019/HW Solutions/HW6.pdfP3.150 In Prob. 3.60 find the torque caused around flange 1 if the center pomt of exit 2 is 1.2

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