OF THE PRESSURE OF FLUIDS ON RIGHT ANGLED PARALLELOGRAMS. 19 



Then, because the point m is at the middle of e, and mn parallel 

 to ad, it follows, that m win \ I; and by reason of the right-angled 

 triangle m r n, we have, from the principles of Plane Trigonometry, 



rm~d^l sin.^ ; 



consequently, the entire pressure upon the plane perpendicularly to 

 its surface, is expressed by 



p ~\ b I* s sin. (f>. 



This is manifest from Problem I. (art. 22), for \l sin. expresses 

 the perpendicular depth of the centre of gravity, and b I the area of 

 the surface pressed ; therefore, the solidity of the fluid column is 



\ I sin. X bl%bl* sin. 0, 



and since s denotes the specific gravity of the fluid, the weight of the 

 column is 



| I sin. <j>XblXs %bl*s sin. <f> ; 



but the perpendicular pressure upon the plane, is equal to the weight 

 of the fluid column ; therefore, we obtain 



p~ J6Z s ssin. 0. (7). 



When the plane of the immersed rectangle is perpendicular to the 

 surface of the fluid, we have in 90, and sin.^> zz: 1 ; consequently, 

 by substitution, the above equation becomes 



P ibl z s. (8). 



These equations are sufficiently simple in their form for practical 

 application, and we shall show hereafter, that they are extremely 

 useful in many important cases of hydrostatical construction. 



34. The practical rules derived from these equations, for determining 

 the pressure in the particular cases, may be expressed as follows. 



1. When the plane is oblique to the horizon. (Eq. 7). 



RULE. Multiply the square of the immersed length of the 

 plane, by the horizontal breadth drawn into the specific 

 gravity of the fluid, and again by the natural sine of the 

 angle of inclination,, and half the product will give the 

 pressure sought. 



2. When the plane is perpendicular to the horizon. (Eq. 8). 



RULE. Multiply the square of the immersed length of the 

 plane, by the horizontal breadth drawn into the specific 

 gravity of the fluid, and half the product will give the 

 pressure sought. 



35. EXAMPLE 4. A rectangular parallelogram, whose sides are re- 

 spectively 1 8 and 3 feet, is immersed in a quiescent body of water, in 

 such a manner, that its shorter side is in contact with the surface, 



c 2 



