Please help me with these homework questions! 1) A spherically shaped balloon ha
ID: 2262898 • Letter: P
Question
Please help me with these homework questions!
1) A spherically shaped balloon has a radius of 10.5 m, and is filled with helium. How much extra mass a cargo can lift, assuming that the skin and the cargo of the balloon have a mass of 950 kg? Neglect the buoyant force on the cargo volume itself.(the density of air is 1.29 kg/m3 and the density of helium is 0.179 kg/m3)
2) Water at a pressure of 3.8 atm at street level flows into an office building at a speed of 0.8 m/s through a pipe 6.8 cm in diameter. The pipes taper down to 2 cm in diameter by the top floor, 30 m above. Calculate the water pressure in such a pipe on the top floor.(g = 9.8 m/s2)
Explanation / Answer
1). buoyant force = weight of cargo + weight of helium + weight of extra mass => pa*V*g = 950*9.8 + p*V*g + mg => 1.29*[(4/3)*pi*10.5^3]*9.8 = 9310 + 0.179*[(4/3)*pi*10.5^3]*9.8 + m*9.8 => m = 4434.56 kg 2). P1 = 3.8 atm = 101325*3.8 Pa = 385035 Pa v1 = 0.8 m/s D1 = 0.068 m z1 = 0 D2 = 0.02 m z2 = 30 m P2 = ? from mass continuity equation; A1*v1 = A2 *v2 => (pi*D1^2/4)*0.7 = (pi*D2^2/4)*v2 => v2 = 0.8*(0.068/0.02)^2 => v2 = 9.248 m/s from Bernoulli's equation; P1 + 0.5*p*v1^2 + p*g*z1 = P2 + 0.5*p*v2^2 + p*g*z2 => 385035 + 0.5*1000*0.8^2 + 0 = P2 + 0.5*1000*9.248^2 + 1000*9.8*30 => P2 = 48592.248 Pa => P2 = 48592.248/101325 atm = 0.4796 atm