Question

A spherical helium balloon of 1.0 metre diameter is released from the ground. The balloon fabric is so thin and light that its weight can be ignored. The balloon's surface is very smooth. The relationship between the drag coefficient and Reynolds number of smooth and rough spheres is shown in Figure 1. (a) State any assumptions required to solve this problem. [1 mark] (b) Find the terminal velocity of the helium balloon as it rises through the air. [18 marks] (c) If the surface of the balloon is modified so that it is rough, would the terminal velocity of the balloon increase or decrease? [1 mark] A graphical solution is acceptable. Figure 1 is repeated on Page 12. Use pair = 1.23 kg/m3, and Phelium = 0.166 kg/m3 and Mair = 1.8 x 10-5 N.sm-2. Smooth Rough 4 2 4 6 8 T 4 6 8 105 1 106 Re Figure 1. Co versus Re for rough and smooth spheres.

Answer 1

ca scumptions linear and gravity force air acting are acting are yo resistance • Near the surlace at the earth an obyer In foll fall in a vaccuum will. a celer are of approximately 9.8mis- cb) 2xm xq where, Now, we lind terminal velocity of a helium balloon. given that diameter 1 166 kg/m² 8x AXC Sony = 1.23 kg/m3 & represents terminal velocity m-is the mass of the object g is the acceleration due to gravity. cds drag, coefficient. ► liste density of the plaid through which object is rising / galling & ~ - profected area of the object. projected 2 V. 2 x S Herreinx Voide 9 Soir X A X Cd Area - Art Ca=0.5 V 12x 0.166 4 XXX (0.5) x 9.8 1.23X TX 3 C0.5 x 0.5

= 1.87 mis er balloon Hence, the terminal velocity of in air is 1.87m's - surface of the balloon is it terminal velocity sough, so decreases