Vízügyi Közlemények, 1944 (26. évfolyam)

1-4. szám - IV. Szakirodalom

(13) g = acceleration constant of gravity.) The study gives information concerning the design in this peculiar case. After the narrow cross section the original flow of water will be critical and will get back into the normal flow through a hydraulic jump. In the case of a weir shown in Fig. 1. the upper — raised — energy line will be with Hf above the level of the threshold, while below the weir the height of the energy line will be H, after the restoration of the original flow conditions. According to the experiments of Dr. A. Testa (Milano) the section endangered with erosion is shortest when the energy measured by 4

H = Hf — H difference is dissipated by hydraulic jump. Calculating the equilibrium of the horizontal components of the forces and impulses acting on the cross sections 1 and 2 preceding and following the hydraulic jump as well as on a water column of unit width and taking into consideration (4) and (Г) we arrive at the relationship (5), from which formula (6) and (7) gives h

2 and the height of the hydraulic jump respectivly. (h

x and h

2 denotes water depths, v

x and v

2 velocities, у is the specific gravity of water, p is the discharge in m

3/sec. m.) By a simplified assumption standing close to reality the length of the hydraulic jump may be taken a,s 1 = 6 (h

2 — h

t). The hydraulic jump develops when h

2 > h

v or on basis of formula (6) if к > h

v that is the flow is critical. The height of the energy line is in the starting and the ending cross section II

1 and H

2 respectively, and the measure of the dissipated energy is JH (formula 9 to 11). From this we arrive with due regard to {4) and (

1

') at (13), and with the aid of (5) to (14), in which naturally h

2 itself is a function of h

1 too (6). In calculating the depth h

1 we start from formula (15) based on (9), (4) and (Г) relationship. By substituting (17), from (16) we arrive at the heterogeneous (18) equation of the third degree. By substituting (20) and (21), which may be retraced to the basic form of (19) and may be solved directly, the roots are h

i

v h

1

2, h

1

3, (23) and (24). Of the three values of the water depth h

v A

u conform with the original normal flow, A

1

3 with the critical flow, while h

1

2 is without physical meaning. After setting of from H

1 the length of the outlet works may be calculated by trials with the aid of (1), (23), (6) and (5), from the water quantity p. By trial, because H

l and the depth of the outlet must be considered in a way that the assumption (14) may also be answered. The author of this paper supplements the procedure in the calculation by trial by direct graphical method according to which the quantities H

v h

2, I and ЛII by the critical depth к and the parameter a (in 28) are expressed. H

1 of (15), after substitution by (29") is expressed by (29); h

2 of (6) after the substitution of (30") by (30); I of (8), (28) and (30) after the substitution of (31") by (31); and finally JH of (14), by substitution of (32") with regard to (29) and (30) by (32). The resulting functions are shown in Fig. 2. The к = 0-467 p'l' makes it possible to directly read the values of к on the logarithmic division. The use of the chart is shown as an example on Fig. 1. (p. 71.) To the normal flow after the dam corresponds h = 2-84 m water depth and H = 300 height of the energy line. To the Q = 150 m

3/sec discharge over a dam head 30 m long and a = 3-94 m high corresponds p = 5 m

3/sec m, and к = 1-37 on chart No. 2. Hereof we receive with the aid of equation (2) the height of the energy line above the dam: a + H

t = Hf = 6-00 m. Proceeding from the assumption J H = Н/ — H = 300 m, we arrive at the vertical A H /к after we substract from the vertical J H the value of к (in lieu of division by substr action), of which at the intersections of curves a, fi, x a

nd Я the values h

v h

2, II

1 and I are received. Hf — Hi = — 0-21 m represents the bottom level of the outlet conduit. CALCUL DIRECT DES DIMENSIONS DES ARRIÈRES-RADIERS ET DES BASSINS D'AMORTISSEMENT. Par G. LAPRA Y, Ingénieur-docteur. (Pages 63 à 72 du texte hongrois.) D. C. 532-51 : 627 43 Les constructions établies dans le lit des cours d'eau modifient essentiellement les conditions d'écoulement du cours d'eau en question. Là, où la vitesse s'accroît, la force d'entraînement augmente, de sorte que l'équilibre primitif étant dérangé, il se produit, dans le cas où l'on ne consoliderait pas le radier, des érosions.