2 10 September 2018, questions PDF

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Summary

practice questions from chapter 2 of R.L.Mott fluid mechanics book....

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Chapter 2 – Example 2.1 • A 25-mm-diameter shaft is pulled through a cylindrical bearing as shown in the figure. The lubricant that fills the 0.3mm gap between the shaft and bearing is oil having a kinematic viscosity of 8×10-4 m2/s and a specific gravity of 0.91. Determine the force P required to pull the shaft at a velocity of 3m/s. Assume the velocity distribution in the gap is linear

Chapter 2 – Example 2.1 – Solution 

𝜏=𝜇 𝑃 = 𝐹 = 𝜏 ∗ 𝐴  𝜇 𝜐 = → 𝜇 = 𝜐𝜌 = 0.91 ∗ 1000 ∗ 8 ∗ 10 = 0.728𝑃𝑎. 𝑠 𝜌 du = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 3𝑚/𝑠 , 𝑑𝑦 = 𝑔𝑎𝑝 = 0.3𝑚𝑚 = 0.0003𝑚 

𝜏 = 0.728 ∗ . = 7280𝑃𝑎 𝐴 = 𝜋𝐷𝐿 = 𝜋*0.025*0.5=0.03926𝑚 P = 𝑆ℎ𝑒𝑎𝑟 𝐹𝑜𝑟𝑐𝑒 𝐹 = 7280 ∗ 0.03926 = 285.88𝑁

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Chapter 2 – Example 2.2 • A large movable plate is located between two large fixed plates as shown in the Fig. Two Newtonian fluids having the viscosities indicated are contained between the plates. Determine the magnitude and direction of the shearing stresses that act on the fixed walls when the moving plate has a velocity of 4m/s as shown. Assume that the velocity distribution between the plates is linear.

Chapter 2 – Example 2.2 – Solution  



therefore, 𝑚 4𝑠 𝑣 𝑁. 𝑠 𝑁 = 13.3  𝜏 = 𝜇 = 0.02  𝑚 𝑚 0.006𝑚 𝑏 𝑚 4𝑠 𝑣 𝑁. 𝑠 𝑁 = 13.3  𝜏 = 𝜇 = 0.01  𝑚 𝑚 0.003𝑚 𝑏

• Shearing stress, 𝜏 = 𝜇

= 𝜇 ,

• Stresses act on fixed walls in direction of moving wall

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