# Page:EB1911 - Volume 14.djvu/57

45
HYDRAULICS

The velocity would be infinite at radius 0, if the current could be conceived to extend to the axis. Now, if the motion is steady, H = pi/G -I-vf/2g = P2/G +v2”/2g; = P2/G 'i”7i2Z'12/"222g; (P2'°P1l/Q =i'i2<I'f1j2/ffl/3§ = l'l'7'12L'1:/}'2Z2g. Hence the pressure increases from the interior outwards, in a way indicated by the pressure columns in fig, 36, the curve through the free surfaces of the pressure columns being, in a radial section, the quasi-hyperbola of the form xy"=c3. This curve is asymptotic to a I horizontal line, H ft. above the line from which the pressures are measured, and to the axis of the current. Free Circular Vortex.-A free circular vortex is a revolving mass of water, in which the stream lines are concentric circles, and in which

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W 1, '/ ', / I I I F1<;.37. which in radial sections is a parabola, and surfaces of equal pressure are paraboloids of revolution (rig. 37). D1ssiPAT1o:~1 or HEAD IN SHOCK § 36. Relation of Pressure and Velocity in a Stream in Steady llloliorz when the Changes of Section of the Slream are Abrupt./Vhen a stream changes section abruptly, rotating eddies are formed which dissipate energy. The energy absorbed in producing rotation is at once abstracted from that effective in causing the flow, and sooner or later it is Wasted by frictional resistances due to the rapid relative motion of the eddying parts of the fluid. In such cases the work thus expended internally in the fluid is too important to be neglected, and the energy thus lost is commonly termed energy lost in shock. Suppose fig. 38 to re resent a stream having such an abrupt change of section. Let Ali CD be normal sections at points where ordinary stream line motion has not been disturbed and where it has been re-established. Let rn, p, v be the area of section. pressure and velocity at AB, and wl, pl, vi corresponding quantities at CD. Then if no work were expended internally, and assuming the stream horizontal, we should have

P/G +112/2g = 1>i/G+v1'/2g- (I) 