Chapter 1 - Section A - Mathcad Solutions 1.4 The equation that relates deg F to deg C is: t(F) = 1.8 t(C) + 32. Solve this equation by setting t(F) = t(C). T 0 Guess solution: Given t = 1.8t 32 1.5 By definition: P= 40 Find ( t) F Ans. F = mass g A P 3000bar D 4mm F P A g 9.807 A m S 4 D mass 2 s 1.6 By definition: P= F 2 F g Note: Pressures are in gauge pressure. A 12.566 mm mass 2 384.4 kg Ans. F = mass g A P 3000atm D 0.17in F P A g 32.174 S 2 D 4 F mass g A ft 2 sec A mass 2 0.023 in 1000.7 lbm Ans. 1.7 Pabs = U g h Patm U 13.535 gm 3 g 9.832 1.8 U 13.535 gm 3 Pabs U g h Patm g 32.243 ft 2 Pabs 176.808 kPa Ans.
H 25.62in s cm Patm 29.86inHg h 56.38cm 2 s cm Patm 101.78kPa m Pabs U g h Patm 1 Pabs 27.22 psia Ans. 1.10 Assume the following: U 13.5 gm g 9.8 3 1.11 2 s cm P 400bar m P h h Ug Ans. 302.3 m The force on a spring is described by: F = Ks x where Ks is the spring constant. First calculate K based on the earth measurement then gMars based on spring measurement on Mars. On Earth: F = mass g = K x g 9.81 mass 0.40kg m x 1.08cm 2 s F mass g F Ks 3.924 N F x Ks 363.333 N m On Mars: x 0.40cm gMars 1.12 Given: FMars mass d P = U g dz FMars K x gMars 0.01 and: FMars mK U= 3 4 u 10 Ans.
Kg M P R T Substituting: P ´ Denver 1 Separating variables and integrating: µ dP = µ P ¶P sea § PDenver ln ¨ After integrating: © Psea ¹ Taking the exponential of both sides and rearranging: Psea 1atm M 29 2 mK = PDenver = Psea gm mol M P d g P= R T dz zDenver ´ µ µ ¶0 M g R T § M g dz © R T ¹ ¨ zDenver § M g z ¨ Denver R T © ¹ e g 9.8 m 2 s 3 R 82.06 cm atm M g zDenver R T PDenver Psea zDenver 1 mi T ( 10 273.15)K mol K 0.194 § M g z ¨ Denver R T ¹ e© PDenver 0.823 atm Ans. PDenver 0.834 bar Ans.
1.13 The same proportionality applies as in Pb. Gearth 32.186 ft gmoon 5.32 2 1.14 gearth gmoon 'learth M 'learth lbm M wmoon M gmoon wmoon costbulb costbulb hr 5.00dollars 10 day 1000hr 18.262 D 1.25ft 113.498 dollars yr Ans. 113.498 lbm 18.767 lbf Ans.
Hr 0.1dollars 70W 10 day kW hr costelec costtotal costbulb costelec 1.15 'lmoon 18.76 2 s s 'learth 'lmoon ft costelec 25.567 dollars yr costtotal 43.829 dollars yr Ans. Mass 250lbm g 32.169 ft 2 s 3 (a) F Patm A mass g (c) 'l 1.7ft 1.18 2 Work EK 1.19 Wdot = Ans. A 424.9 ft lbf 2 S 2 D 4 A 4 110.054 kPa 'EP mass' g l 'EP m s 1000 kJ Work 1000 kJ Ans. Mass' g h 0.91 0.92 time Wdot 200W g 9.8 m 2 s 4 m 2 s Work EK Ans. G 9.813 Work F 'l u 40 2 3 4.8691 u 10 ft lbf Ans.
1.909 u 10 N F Pabs mass 1250kg mass u 16.208 psia 'PE A 1.227 ft Ans. 'PE mass' g l F 1 3 mass 150kg 'l 0.83m EK A Work (a) F Patm A mass g (c) 2 Work F 'l Patm 101.57kPa (b) Pabs D 2.8642 u 10 lbf Pabs D 0.47m 1.16 4 F F A (b) Pabs S A Patm 30.12inHg 'h 50m 2 0.173 m Ans. 15.848 kJ Ans. 1.222 kJ Ans. Wdot mdot 1.22 a) costcoal mdot g 'h 0.91 0.92 0.488 25.00 ton 29 costgasoline costcoal MJ 0.95 GJ kg s Ans.
1 kg 2.00 gal 37 GJ costgasoline 14.28 GJ 1 3 m costelectricity 0.1000 kW hr costelectricity 27.778 GJ 1 b) The electrical energy can directly be converted to other forms of energy whereas the coal and gasoline would typically need to be converted to heat and then into some other form of energy before being useful. The obvious advantage of coal is that it is cheap if it is used as a heat source. Otherwise it is messy to handle and bulky for tranport and storage. Gasoline is an important transportation fuel. It is more convenient to transport and store than coal.
It can be used to generate electricity by burning it but the efficiency is limited. However, fuel cells are currently being developed which will allow for the conversion of gasoline to electricity by chemical means, a more efficient process.
Electricity has the most uses though it is expensive. It is easy to transport but expensive to store. As a transportation fuel it is clean but batteries to store it on-board have limited capacity and are heavy. 5 1.24 Use the Matcad genfit function to fit the data to Antoine's equation. The genfit function requires the first derivatives of the function with respect to the parameters being fitted.
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