Hidrológiai Közlöny 1976 (56. évfolyam)

1. szám - Dr. Bogárdi János: Elmélet, oktatás és gyakorlat a hidraulikában és hidromechanikában

Dr. Bogárdi, L. J.: Theory, education and practice in hydraulics Hidrológiai Közlöny 1976. 1. sz. 9 must be informed about the limit values within which a particular expression is valid. The units of measurement of the variables involved in the expressions must be specified positively. The simplifying assumptions introduced in deriving the expressions must also be specified precisely. The shortcomings often experienced in these respects must be charged against the professionals engaged" in theory and research. In practical work, errors and mistakes are inevitable. Hydraulic engineers use expressions without being informed on their origin or range of applicability. Relations are extended although this would be impermissible according to research. His confidence in material written and published may be exaggerated. Methods involving additional work or new advances in technological development are accepted with reservation only. The relationship between scientific research and practice is indeed a rather loose one. Attempts have been made long ago at correlating these two activities, which would imply substantially the more efficient practical utilisation of advances in theory and research. The addition of some guidelines for both the researchers and the practicing engineers would be extremely beneficial by eliminating the errors observable in each of the two different activities. In hydraulics theory, education and practical application are organically interrelated. As demonstrated clearly by the foregoing considerations, the greatest help can be obtained by adopting the uniform physical approach. The advantages thereof in the teaching of theoretical and practical hydraulics have been detailed before. A few examples will be presented subsequently to demonstrate that the physical approach is essential also in practical hydraulics. Besides a few extremely simple, familiar and perhaps even primitive examples a few more complex problems will also be described, which however, may become essential for the practicing engineers in the near future already. The dimensioning of tanks for fluid pressure presents a problem commonly encountered. The lower, horizontal part of an "L"-shaped vessel filled with fluid, must be dimensioned, evidently, for the pressure resulting from the full height of the water column. On the other hand, when dimensioning the load-bearing structure supporting the fluid-filled "L"-shaped vessel, only the weight of the actual fluid volume must be introduced besides the dead weight of the vessel. In this case it is immaterial, whether the distribution of fluid pressure as a physical phenomenon has occured or not to the designer. Nevertheless, this primitive problem is also solved by the physical approach. The velocity v of a fluid jet issuing from a tank at the depth h below the fluid surface is obtained with fair approximation as v ' cpY 2gh (64) of the orifice. In Eq. (64) velocity is described in terms of the gravity force only, neglecting effects due to inertia, friction, capillarity and elasticity, which are indeed smaller by orders of magnitude than the influence of gravity on velocity. Allowance for these insignificant influences is also made by the coefficient cp, as demonstrated by the excellent agreement between the velocities computed and actually observed. The physical approach is, however, necessary in such cases as well. Extreme conditions may be encountered, where, for instance the frictional forces due to the viscosity of the fluid are no more negligible. A primitive error may result from treating velocity

—which is actually a vector quantity

—as a scalar in the absence of the proper physical approach. The rate of fluid flow, in the case of water the discharge, is denoted in practical hydraulic as Q = vF, i.e., as the product of velocity and the cross-sectional area of flow, assuming the velocity v to be perpendicular to the surface F. If this is not the case, the result will be obviously an incorrect one. Under the physical approach, regarding the fluid discharge as the current in unit time of the volume [L

3] as an extensive quantity, the possibility of this error is excluded. In fact the volume current is the surface integral of the velocity vector Q= -J v dF (65) where dF is the product of the absolute magnitude of the surface and of the unit vector perpendicular thereto. Eq. (65) is an inherent guarantee that the surface is multiplied by the velocity component perpendicular thereto, since the scalar product of two vectors is involved. Repeated mention has been made in the foregoing of dimensional homogeneity.. The observation thereof is essential in practical hydraulics as well. AH physically valid equations must be consistent as regards dimensions. Dimensional consistency is checked without undue difficulty. A much more common source of errors in the individual formulae is the use of incorrect units of measurement for the variables. In terms of the depth y

x of the velocity ij, upstream of the hydraulic jump, and of gravitational acceleration g the conjugate depth ?/

2 downstream of the jump is obtained from the familiar formula -2/1 + y*

=• (66) With the value ö

f=9.81 m/s

2 the computation formula = 0.s[-y

x+}Iyt+0.Z\5vly

x) (67) Concerning <p the only statement which can be made is that its magnitude depends on the shape is obtained. A formally similar expression is obtained if the value <7=32.2 ft/s

2 of the foot-