By G. K. Batchelor
First released in 1967, Professor Batchelor's vintage paintings continues to be one of many prime texts on fluid dynamics. His cautious presentation of the underlying theories of fluids continues to be well timed and appropriate, even today of just about unlimited desktop energy. This reissue guarantees new iteration of graduate scholars stories the beauty of Professor Batchelor's writing.
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The specific heat thus depends on the ratio oP/Of). that is, on the choice of direction of the chan~e from A. p1 Isothermal change J I l j ~. 1. Indicator diagram for the equilibrium states of a fluid. 5·5) Now 8T varies sinusoidally as the point representing the final state moves round a circle of small radius centred on A, being zero on the isotherm through A and a maximum in a direction m normal to the isotherm. Likewise oQ varies sinusoidally, being zero on the adiabatic line through A and a maximum in a direction n normal to it.
2). When the distribution of pF does have the form required for equilibrium, p is constant over any surface which is everywhere normal to the body force. The nature of the restriction on p and F takes a more specific form in the common case in which the body force per unit mass (F) represents a conservative field and can be written as - V'l', where 'l' is the potential energy per unit mass associated with this field. 3) equilibrium is or, on taking the curl of both sides, (Vp) x (V'l') = o. Thus the level-surfaces of p and 'l' must coincide, and, when this condition is satisfied, these are also the level surfaces of p and we may write dp/d'Y = -pry).
Suppose, for instance, that a vessel containing fluid of non-uniform density is rotating steadily about the vertical z-axis and that the fluid has taken up the same steady rotation. Q2(X2+y2)1 in a horizontal plane due to the effective centrifugal force. 1). For equilibrium it is necessary that p be constant on each of these paraboloids; and then p is also constant on each paraboloid. If now a solid body, say a sphere of uniform density, is immersed in the fluid in this vessel and is at rest relative to it, the fluid exerts a certain buoyancy force on the body.