In TableF.2(front of book), find the hydrostatic equation. For each form of the

Question

In TableF.2(front of book), find the hydrostatic equation. For each form of the equation that appears, but he name, symbol, and primary dimensions of each variable. What is the approximate mass in units of slags for a 2-liter bottle of water a typical adult male? a typical automobile. A spherical tank is being designed to hold 10 moles of methane gas at a pressure of 2 bar and a temperature of 70degreeR. what diameter spherical tank should be used? What is the (a) specific weight, and (b) density of air at an absolute pressure of 600 kPa and a temperature of 50degreeC? Adesign team is developing a prototype CO_2 cartridge for a manufacturer of rubber rafts. This cartridge will alllow a user to quickly inflabe a raft. A typical raft is shown in the sketch. Assume a raft inflation pressure of 3 psi (this means that the absolute pressure is 3 psi greter than local atmospheric pressure). Estimate the volume of the raft and the mass of CO_2 in grams in the prototype cartidge. A team is designing a helium-filled balloon that wil fly to an altitude of 80,000 ft. As the balloon ascends, the upward force (buoyant force) will need to exceed the total weight. Thusm, weight is critical. Estimate the weight (in newtons) of the helium inside the ballcon. The balloon is inflated at a site where the atmpspheric pressure is 0.89 bar and the temperature is 32degreeC. When inflated prior to launch, the balloon is spherical (radius 1.3 m) and the inflation pressure equals the local atmospheric pressure.

Explanation / Answer

1 slug = 14.59 g under stadard gravity

a) 2 Ltr ater bottle weighs 2 Kg = 2/14.59 = 0.137 slugs

b) average adult weighs 60 Kg = 60/14.59 = 4.11 slugs

c) average autmobile weighs 1500Kg = 1500/14.59 = 102.81 sugs

1.33

PV= nRT

T = 70 F = 21.11C = 294.1 K

R = 8.314 n = 10 P = 2bar = 2.0e+5 Pa

V = nRT/P = 10*8.314*294.1/2.0e+5 = 0.1222 cu.m

    = (4/3)piR3 - spherical tank, R radius of the tank

R = 66.03 cm

Density of air = 1.2754 kg/m3 at 0degC and 100 kPa

PV = nRT

V1/v2 = T1P2/T2P1

density is inversely proportional to Volume mass being constant

D2/D1 = T1P2/T2P1

density at 600kPa and 50 degC

D2 = 1.2754 *273*600/(273+50)*100 = 6.4678 kg/m3

specific weigh = 6.4678 Kg in SI units.

1.41:

The raft is made of cylindrical tube of 0.45 m dia

external dimensions = 4.0 m X2.5 m

internal dimensions   = 3.1 X 1.6 m

average length of the outer tube = 2(3.55+2.05) = 11.2 m

there are two pieces inside each of length = 1.6 m

total length of the tube = 11.2+2*1.6 = 14.4 m

volume V = 14.4*pi*(0.45/2)2 = 2.29 cu.m

pressure = 3psi +atm = 3*6.89 kpa +101 kPa = 121.67 kPa

we assume the temp 300 K     normal temp.

n = PV/RT = 121.67e+3 * 2.29 /(8.314*300) = 111.71 moles

1 mole of CO2 = 12+8*2 = 38 gms

mass of CO-2 = 38*111.71 = 4.245 kg

1.42:

pressure P = 0.89 bar = 89 kPa T =22 degC

radius r = 1.3 m

volume V = (4/3)*pi*(1.3)3 = 9.20 cu.m

n = PV/RT = 89e+3*9.2/(8.314*295)= 333.85 moles

mass of He = 333.85*4 = 1.335 kg

                      = 13.1 N

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