Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/128

to the body an equal and opposite force has to be applied to the external boundary of the fluid; thus, if a stream-line body of the same specific gravity as the fluid be started from rest from a boundary surface, during the application of the accelerative force there will be a region of diminished pressure in the neighbourhood, whose sum is in effect of equal value and opposite sign to the applied force. (Compare Chap. I., § 5.)

§ 82. Pressure Distribution. Fluid Tension as Hypothesis.—The distribution of pressure in the field of flow of a fluid in a state of steady motion can be ascertained immediately from the distribu- tion of kinetic energy if we assume the principle of work.

The change in the velocity of any element of the fluid in passing from one to another part of the field is due to the difference of pressure on its boundary surfaces, and consequently, on the principle of Torricelli (which follows from the assumption of conservation of mechanical energy), the difference of pressure between any two points is that of the difference of "head" corresponding to the values of the velocity at the two points. Thus if the pressure where the motion is nil be taken as zero, the pressure at every point in the field will be proportional to $-(v^{2})$.

Now a minus pressure constitutes a tension, a kind of stress that actual fluids can only support within very narrow limits; we may, however, by subjecting the whole field to a superposed hydrostatic pressure $p$ of sufficient magnitude, do away with minus pressure throughout the region, the condition being that for every point $p\ {\boldsymbol {-}}\ nv^{2}$ is positive, where n is a constant. The pressure under these circumstances becomes, where the motion is nil, equal to the applied hydrostatic pressure $p$.

The objection to the existence of a tension of any desired magnitude in the fluid is entirely based on the behaviour and properties of real fluids, with which we are not for the time being concerned; it is a mere matter of hypothesis and definition to provide that the ideal fluid shall support without cavitation any

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