OF THE CENTRE OF PRESSURE. 



415 



Suppose m to be the centre of pres- 

 sure, and make mb equal to twice 

 me; then by equation (304), the 

 point b must coincide with the sur- 

 face of the fluid. 



Through the point b and parallel 

 to B or cc?, draw the straight line 

 rs, which marks the height to which 

 the vessel must be filled with fluid, 

 before the side is forced open. 



C 



Put b = au, the breadth of the loose side of the vessel, 



S zz en, the distance from the bottom at which the force is 



applied, 



yzz: the magnitude of the force applied at the point n, 

 s zr the specific gravity of the fluid contained in the vessel, 

 p HZ the pressure of the fluid against its side, and 

 z = cb, the height to which the fluid rises. 



Then, by the principle indicated in equation (8), Problem III. 

 Chapter II. we have 



and this takes place at the centre of pressure, which, according to 

 equation (304), is situated at two thirds of the depth below the 

 surface, and consequently, its effect to turn the side andc on the 

 hinges e and /*, is, according to the principle of the lever, expressed by 



Now, the effect of the force applied at w, to prevent the side from 

 being thrust open by the pressure of the fluid, is expressed by the 

 magnitude of the given force, drawn into en the length of the lever 

 on which it acts, and is precisely equal to the effect of the fluid 

 acting at the centre of pressure ; hence we get 



/8 =#*,; 

 and by division this becomes 



Z - 



Z - -7 * 



bs 

 from which, by extracting the cube root, we obtain 



bs 



