MathAdvanced MathQ&A Libraryonsequenn is then found I., Ic-rting ξ (33) lhe escape velocity of the escape velocity neglects the effect of air resistance, so the including the effect of air resistance) is somewhat higher. On the other 6.9 mils, or 11.1 km/s The numerical value of , is approximately The preceding calculation of the escape ve tance above sea level before being launched. Both gravitational and frictional ereby reduced; air resistance, in particular, diminishes quite rapidly with increasing eep in mind also that it may well be impractical to impart too large an instantaneously; space vehicles, for instance, receive their initial acceleration pe velocity can be significantly reduced if the body is transported considerable dis forces are th initial velocity during a period of a few minutes. PROBLEMS Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 L/min, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye inthe tank reaches 1% of its original value. 2. A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression in terms of y for the amount of salt in the tank at any time t. Also find the limiting amount of salt in the tank as t-oo 3. A tank originally contains 100 gal of fresh water. Then water containing lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving at the same rate. F salt in the tank at the end of an additional 10 min. mou 4. A tank with a capacity of 500 gal originally contains 200 gal of w lb al th in solution. Water containing 1 lb of salt per gallon entering a the mixture is allowed to flow out of the tank of salt in the tank at any time prior to the in Find the concentration (in pounds per gall of overflowing. Compare this concentrati the tank had infinite capacity th he 5. A tank contains 100 gal of water and S

Advanced Engineering Mathematics

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ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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