Tutorial No. 1
2.15 A team is designing a helium-filled balloon that will fly to an altitude of 24,000 m. As the balloon ascends, the upward force (buoyant force) will need to exceed the total weight. Thus, weight is critical. Estimate the weight (in newtons) of the helium inside the balloon. The balloon is inflated at a site where the atmospheric pressure is 0.89 bar and the temperature is 22°C. When inflated prior to launch, the balloon is spherical (radius 1.3 m) and the inflation pressure equals the local atmospheric pressure. 2.29 The viscosity of SAE 10W-30 motor oil at 38°C is 0.067 N · s/m2 and at 99°C is 0.011 N · s/m2. Using Eq. 2.8 for interpolation, find the viscosity at 60°C. Compare this value with that obtained by linear interpolation. 2.34 The velocity distribution for water (20°C) near a wall is given by u = a(y/b)1/6, where a = 10 m/s, b = 2 mm, and y is the distance from the wall in mm. Determine the shear stress in the water at y = 1 mm.
2.43 One type of viscometer involves the use of a rotating cylinder inside a fixed cylinder. The gap between the cylinders must be very small to achieve a linear velocity distribution in the liquid. (Assume the maximum spacing for proper operation is 1.5mm). Design a viscometer that will be used to measure the viscosity of motor oil from 283K to 365K.
2.58 The surface tension of a liquid is being measured with a ring as shown in Fig. 2.8d. The ring has an outside diameter of 10 cm and an inside diameter of 9.5 cm. The mass of the ring is 10 g. The force required to pull the ring from the liquid is the weight corresponding to a mass of 16 g. What is the surface tension of the liquid (in N/m)?