238 REPORT — 1875. 



At the point of exit A the fluid is under no pressure whatever, since there 

 is no reacting force to maintain any pressure ; each particle of fluid in the issuing 

 jet is rushing on on its own account, neither giving nor receiving pressure from its 

 neighbours. We know, however, what force it has taken to give the velocity 

 which the fluid has at the point of issue A, and we measure this force by the 

 pressure, or head of fluid, lost. In the case we are considering, this head is 

 represented by the height of the fluid in the cistern, or by the height AD._ 



Within the cistern, at the point E, on the same level as A the point of issue — at 

 this point E within the cistern, we have the pressure due to the head of fluid equal 

 to AD, but we have no velocity, at any rate the velocity is so small as to be in- 

 appreciable ; and at the point of issue A we have no pressure at all, but we have 

 what is termed the "velocity due to the head." 



Let us suppose that at the points A, B, C, and E, gauge-glasses or stand-pipes 

 are attached so that the fluid in each may rise to a height corresponding with the 

 pressure within the pipe or nozzle at the point of attachment. 



The gauge-glass attached at A will show no pressure, thus indicating that the 

 entire head AD has been expended in producing the velocitj^ at the point A. 



At the point B, as the sectional area is twice, the velocity is one half that at A; 

 Now the head required to produce velocity varies as the square of the velocity to 

 be produced ; in other words, to produce half the velocity requires one quarter of 

 the head ; thus of the whole head AD available, one quarter only, or GD, has been 

 absorbed in developing the velocity at B, and the remainder of the pressure, which 

 will be represented by the head BG, will be sensible at the point B, and will be 

 exhibited in the gauge-glass attached at that point. 



Again, as the pipe at is four times the area that it is at A, it follows that, of the 

 whole head AD, one sixteenth part onlj', or HD, has been absorbed in developing 

 the velocity at C, and the remainder of the pressure, which will be represented 

 by the head CH, will be sensible at the pomt 0, and will be exhibited in the 

 gauge-glass attached at that point. 



In the case I have chosen for illustration the small end. A, of the nozzle, is open 

 and discharging freely, and the pressure at that point is therefore nil. But the 

 absolute difierences of pressure at each point of the pipe or nozzle will be 

 precisely the same (as long as the same quantity of fluid is flowing through it 

 per second), however great be the absolute pressures throughout. 



Thus, suppose that from the end of the nozzle at A a pipe of the same diameter^ 

 and of uniform diameter throughout its length, is curved upwards so that the end 

 of it, I, is two feet higher than A, as shown in Plate XII. fig. -35, if the level of the 

 cistern is also raised two feet, namely to the level marked J, instead of D, we shall 

 have the same deliveiy of fluid as before ; and the differences between the pres- 

 sures at each point will be the'same as before. 



If we add 50 feet instead of 2 feet to the head in the cistern ; and raise 1 to 60 

 feet, instead of 2 feet above the nozzle, the diflerences of head or pressure vsdll 

 still be the same, the head at A being 50 feet, that at B being EG-f 50 feet, that 

 at C, CII-l-50 feet, and that at E (the cistern-level) ED-f 50 feet. 



To put the case into actual fig.m'es, suppose the sectional area at A to be 1 square 

 inch ; that at B, 2 square inches ; and that at C, 4 square inches ; and suppose thatthe 

 fluid is passing through the nozzle at the rate of one ninth of a cubic foot per second : 

 we shall have a velocity at A of 16 feet per second — to generate which would 

 require a difference of pressure between E and A equivalent to 4 feet of vertical 

 head. The velocity at B will be 8 feet per second, which would require a difference 

 between E and B equivalent to 1 foot of head. That at C wiU be 4 feet per 

 second, and will require a difference of pressure equivalent to 3 inches of head. If 

 the pressure at A be zero, the pressures at B, C, and E will be 3 feet, 3 feet 9 inches, 

 and 4 feet respectively. If the pressure at A be 1 foot, the pressures at B, 0, and 

 E will be 4 feet, 4 feet 9 inches, and 6 feet respectively ; and if the pressure at A 

 be 1000 feet,",the_pressures at B, C, and E will be 1003 feet, 1003 feet 9 inches, and 

 1004 feet respectively, always supposing the quantity of fluid passing per second to 

 be the same. If the quantity be different, the absolute differences of pressure will be 

 different, but will be relatively the same. If, for instance, the quantity flowing 

 per second be doubled, the velocity at each point will be doubled, and the differences 



