The height of a cylindrical tank, containing 15 lb of gas at 70 psia and 115 Farenheit, IS TRIPLE ITS DIAMETER; the gas constant is R = 45 ft lbf/lbm R. find.
a) the tankdiameter in ft.
b)the tank height in ft.
W=15 lbm, P= 70 psia, T=115 F, H=3D, R = 45 ft lbf/lbm°R
Volume of cylireler
"V=\\frac{\u03c0}{4} D^2\\times H=\\frac{\u03c0}{4}D^2\\times3D=\\frac{3\u03c0}{4}D^3\\\\\n\nV=\\frac{3}{4}\u03c0D^3"
1F=459.67R
1ft=12inches
So, T=115F=115+459.67=574.67R
"Psia=\\frac{lbf}{in^2}=\\frac{lbf}{(\\frac{1}{12})^2ft^2}"
By ideal gas equation
PV=mrt
"\\frac{70}{ (\\frac{1}{12})^2}( \\frac{lbf}{ft^2})\\times \\frac {3\u03c0}{4}D^3(ft^3)=15(lbm)\\times45(\\frac{lbf-ft}{lbm\u00b0R})\\times 574.67\u00b0R"
Unit of bath side is balanced
Diametr D=2.537 ft
Height "H=3\\times D=3\\times 2.537"
H=7.6115ft
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