4 Ml ASl'HE OF 



5. Solidifying a Fluid.// a mass of fluid, be at 

 rest, any portion of it may be supposed to become 

 solid without affecting its equilibrium, or the pressure 

 of the surrounding fluid. 



For there will be no alteration in the forces acting on the 

 fluid, and the action between the solidified portion and the 

 rest of the fluid, or between the solidified portion and any 

 surface with which it may be in contact, will still be nor- 

 mal to its surface (Art. 4) ; therefore the equilibrium of the 

 solid can be considered as maintained by the external forces 

 which act upon it, and the pressure of the remaining fluid. 



This proposition enables us to employ the principles of 

 statics in the discussion of the equilibrium of fluids. 



6. Measure of the Pressure of Fluids The press- 

 ure of a fluid on a plane is measured, when uniform over 

 the plane, by the force exerted on a unit of area. Consider 

 a mass of fluid at rest under the action of any forces, 

 and let A be the area of a plane surface in contact with the 

 fluid, and P the force which is required to counterbalance 

 the action of the fluid upon A. Then if the action of the 



p 



fluid upon A be uniform, -r is the pressure on each unit of 



A. 



the area A, and this is usually represented by p. 



If the pressure be variable, as, for instance, on the verti- 

 cal side of a vessel, it must be considered as varying con- 

 tinuously from point to point of the area A, and the pressure 

 at any point is measured by that which would be exerted on 

 a unit of area, supposing the pressure over the whole unit 

 to be exerted at the same rate as at the point considered. 

 If we suppose the area A, and the pressure P, to diminish 

 indefinitely, the pressure may l)e regarded as uniform on the 



dP 

 intinitesiiniil area dA, and we shall have -v-, = p to express 



the rate of pressure at the point considered. 



