An Introduction to Engineering Systems by Samuel Seely

By Samuel Seely

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This law relates the heat flow to the gradient of the temperature {see Fig. l-44a), Q = KA (01~e*> (Joules/sec) (1-71) where Q = heat flow, Joules/sec, K = thermal conductivity, Joules/m-sec-deg, A = area normal to heat flow, m2, / = length of conductor, m, 6 = temperature, deg K. The direction of the heat flow is from the region of high temperature to the region of low temperature. The form of this law is identical with Ohm's law, Eq. (1-22), which relates the current in an electric circuit and the difference of potential.

Quantitative aspects of duality in electrical systems. corresponding pair of equations on a horizontal line of this table are said to be dually related. There is a systematic interchange of the variables and with similar mathematical form. From this it is seen that C and L, G and R are dually related. Note carefully, however, that duality implies only that the mathematical representations are similar in form; no aspect of equiv­ alence is implied. The Ideal Mass Element 1-b 1-12 29 MECHANICAL ELEMENTS THE IDEAL MASS ELEMENT When considered in terms of Newton's second law of motion, the mass M is defined by the expression, dv d^x f=M-^ dt = M-jz df = Ma (Newtons) (1-32) which relates the force (a through variable) with the acceleration (an across variable).

1-42. Fluid (gas) resistance and capacitance. The turbulent gas flow resistance is defined as, R= (sec/m2) %' (1-63) It is not possible to easily calculate R from Eq. (1-63) because the expan­ sion factor Y depends on the pressure. In this case it is easier to determine resistance from a plot of pressure against flow for any particular device. For laminar gasflowthrough tubes and pipes, Eq. (1-56) can be used. To discuss the capacitance of a pressure vessel, we first write a flow law for the pressure vessel of Fig.

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