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?

5. One way to study the surface tension effects in a liquid/solid system is to dip a pair of parallel
plates into the container of the liquid. How far up in a pair of parallel glass plates, 0.3 mm
apart, would water at 40oC be drawn up?

6. A 5 kg block is supported on a thin film of an unknown liquid 0.2 mm thick on an incline of 10o.
Determine the viscosity of the liquid if the terminal velocity is 5.678 m/s. Assume the velocity
distribution in the gap is linear, and the area of the block in contact with the oil is 0.25 m2.
What is the possible identity of the liquid if the temperature is 20°C?

Explanation / Answer

The increase in the glass’ volume is: 6 (glass) (glass)(1 3 T) 1.0 [1 3 2 10 (50)] 1.0003 L V V f i a - = + ? = + × × = The increase in the mercury’s volume is: 6 (1 3 T) 1.0 [1 3 61 10 (50)] 1.0092 L V V f i a - = + ? = + × × = So, the volume of mercury that overflows is: ? = - = V 1.0092 1.0003 0.0089 L. For Water : Heat needed Q 1.0 4183 (70 20) 2.1 10 J For Copper: Heat needed Q 0.8 400 (70 20) 1.6 10 J total heat needed 2.1 10 J 1.6 10 J 2.3 10 J

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