PRESSURE 17 



At some point as B, where the depth has increased to D and the velocity 

 has decreased to F, the velocity head will have diminished to F^/2g. 

 Since the quantity of water flowing past each point is the same, let 

 Q = volume of water per foot in width of the conduit, then 



Q = ViDi = VD [201] 



or 



y = ^ [202] 



By Bernoulli's theorem the static pressure at B then equals 

 Fi^ F^ FiV Z)A 



In general, this pressure at B would not equal D exactly, but would 

 be something greater, as BF. By means of the above expression, the 

 static pressure corresponding to each depth can be easily calculated for 

 given conditions. This has been done for Fig. 201. 



The resulting static pressures, when plotted above the base AM, give 

 the curve EFGH. This curve, which crosses the surface of the water 

 at E and H, indicates relations of great fundamental importance which 

 should be carefully noted. At E the static pressure on the bottom is 

 exactly that due to the depth of water AE. As soon as the velocity is 

 reduced and part of the velocity head is thus converted into pressure, 

 the pressure on the bottom is greater than that due to the depth of the 

 water alone. Thus at P the pressure is that caused by a head GP. 

 This means that at the point N there is a pressure against the upper 

 bounding surface of the water equal to that caused by a head ON. If a 

 small piezometer tube should be inserted through the upper surface at N, 

 the water would rise in it to the level of G. This pressure tends to burst 

 the cover off the conduit. The curve EFGH is really the hydraulic 

 grade line through the expanding section. 



This interior bursting pressure against the upper surface begins with 

 zero at E and increases, very rapidly at first, and then more slowly, 

 until it reaches a maximum value such as GN at N. From this point 

 onward it gradually decreases until it again reaches zero at H. The 

 pressure on the bottom at M is again exactly that caused by the depth 

 of the water. 



As the velocity decreases between E and N, the corresponding diminu- 

 tion of velocity head is more than enough to raise the water along the 

 rigid, slanting, upper boundary surface, and hence there is an accumula- 

 tion of excess static pressure. As the velocity decreases from N to H^ 



