3. A 500 ml cylindrical mug is filled level with the top of the mug with 90°C wa

Question

3. A 500 ml cylindrical mug is filled level with the top of the mug with 90°C water. What is the water level relative to the top of the mug if the water is cooled to 20°C? The diameter of the mug is 10 cm. Ignore any surface tension effects.

4. A 4 cm diameter shaft is held in place by a bushing with an inside diameter of 4.1 cm. The bushing has a length of 1.5 cm and is lubricated with SAE 50 Oil at 80oC. If the shaft is rotated at a constant speed of 4500 rpm:

a. What torque must be applied to the shaft to overcome the fluid shear stress to
maintain this rotational speed?

b. What power (in W) would be required to maintain this speed?

Explanation / Answer

As the temperature of water decreases, its density increases upto 4 deg. then there is anomalous expansion of water, thats the reason for density of ice less than than density of water. But here its only upto 20 celsius. Hence density increases, so for same mass of water volume decreases, so water level decreases. If u want to know water peroperties accurately, go to http://www.waterproperties.eu
Atm Pr = 101.325 kPa = 101325 Pa
Temp to get sp.volume (reciprocal of density)

From Shigley's Mechanical Engg Design by Keith Nisbett and Richard Budynas
Fig 12-12 Lubrication and Journal bearings chapter
= 4 X 10-6 Reyn at 800C or 176 F, = 4 X 10-6 X 6890 Pas = 0.02756 Pas

c = Radial clearance = (4.1-4)/2 cm = 0.0005 m

r = Radius of shaft = 2 cm = 0.02 m

length of bearing = 1.5 cm = 0.015 m

N = 4500rpm = (4500)/(2.60) = 11.9366 rad/s

T (torque) = (42r3lN)/c = 0.019584 Nm

Power = T = 0.019584*11.9366 = 0.23377W

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