18 HYDRAULICS AND ITS APPLICATIONS 



It foll.)v\s from these theorems that the free surface of still water is a 



surface of equal pressure, and that all equipotential surfaces in the fluid 



trullt'l u> this. This surface is not plane, but is everywhere normal 



Action of the force of gravitation, and therefore to the direction 



of a plumb line. 



ART. 8. TRANSMISSIBILITY OF PRESSURE IN A FLUID. 



If a pressure be applied to the surface of a fluid, this pressure is trans- 

 mitted equally to all parts of the fluid. This may be seen by considering 

 a closed vessel filled with water, and fitted with a piston of area A, to 

 which a force P is applied, producing a pressure intensity at this point of 

 P-^-A. Considering any other area A of the surface, the two may be 

 supposed connected by a cylinder of the fluid, having imaginary 



boundaries (Fig. 6). 



Suppose piston P to be displaced 

 through a small distance x. Then in 

 virtue of the incompressibility of the 

 fluid, Q will be displaced through the 

 same distance. Also, since the reaction 

 of the cylinder walls is everywhere per- 

 ,FJG. 6. pendicular to the direction of motion of 



the contained fluid, no work is done 



against this reaction, and in consequence the work done by P = work 

 done on Q. Since the areas and displacements of P and Q are the 

 same, the pressure intensities over their surfaces, introduced by the 

 action of the external forces, must also be equal. The total pressure 

 intensity at either P or Q will then be obtained by adding to the pressure 

 produced by the force P, that due to the weight of the liquid. Altering 

 the plane of the pistons at P and Q will evidently not affect the pressure 

 intensity on either surface. 



This property is taken advantage of in many hydraulic machines, 

 notably in Bramah's Hydraulic Press, and in machines of a like type. 



In the Hydraulic Press, illustrated diagrammatically in Fig. 7, water is 

 forced by means of a small pump F, whose plunger has an area a, into 

 the cylinder C of the press whose area is A. Neglecting friction, a force 



P, applied to the plunger of the force pump, will then produce a pressure 



p 

 intensity of in the pump and press cylinder, and hence a force of Q 



P -on the press plunger. A particular case of the transmissibility of 



