pub20-h1.2 - Empirical stage-discharge equations of this...

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Empirical stage-discharge equations of this type (Equation 1-66) have always been derived for one particular structure, and are valid for that structure only. If such a structure is installed in the field, care should be taken to copy the dimensions of the tested original as accurately as possible. 1.12 Orifices The flow of water through an orifice is illustrated in Figure 1.20. Water approaches the orifice with a relatively low velocity, passes through a zone of accelerated flow, and issues from the orifice as a contracted jet. If the orifice discharges free into the air, there is modular flow and the orifice is said to have free discharge; if the orifice discharges under water it is known as a submerged orifice. If the orifice is not too close to the bottom, sides, or water surface of the approach channel, the water particles approach the orifice along uniformly converging streamlines from all directions. Since these particles cannot abruptly change their direction of flow upon leaving the orifice, they cause the jet to contract. The section where contraction of the jet is maximal is known as the vena contracta. The vena contracta of a circular orifice is about half thedkmeter of the orifice itself. I_c___ If-e-free aischarging orifice shown in Figure 1.20 discharges under the average head HI (if H, >> w) and that the pressure in the jet is atmospheric, we may apply Bernoulli’s theorem - -- HI = (h, + vI2/2g) = v2/2g (1 -67) Hence v = ,/2gHI (1 -68) This relationship between v and fi was first established experimentally in 1643 by Torricelli. Figure I .20 The free discharging jet 42
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I I I Figure I .21 Rectangular orifice If we introduce a C,-value to correct for the velocity head and a C,-value to correct for the assumptions made above, we may write V = Cd c, J2ghI (1 -69) According to Equation 1-2, the discharge through the orifice equals the product of the velocity and the area at the vena contracta. This area is less than’the orifice area, the ratio between the two being called the contraction coefficient, 6. Therefore Q = CdCv6Am -70) i The product of cd, C, and 6 is called the effective discharge coefficient Ce. Equation 1-70 may therefore be written as Q = CAm (1-71) ~ ~ Proximity of a boundinp surface of the approach channel on one side of the orifice erevents the free approach of water and the contraction is partially suppressed on -e. If the orifice edge is flush with the sides or bottom of the approach channel, the contraction along this edge is fully suppressed. The contraction coefficient, how- ever, does not vary greatly with the length of orifice perimeter that has suppressed contraction. If there is suppression of contraction on one or more edges of the orifice and full contraction on at least one remaining edge, more water will approach the’ orifice with a flow parallel to the face of the orifice plate on the remaining edge(s) and cause an increased contraction, which will compensate for the effect of partially or fully suppressed contraction.
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This note was uploaded on 03/30/2012 for the course FLV 231 taught by Professor Yousry during the Spring '12 term at Qatar University.

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pub20-h1.2 - Empirical stage-discharge equations of this...

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