Lecture 4 OPEN-CHANNEL FLOWFluid Mechanics: Fundamentals and ApplicationsThird Edition in SI Units Yunus A. Cengel, John M. CimbalaMcGraw-Hill, 2014Prof Taha TaherCopyright 2014 McGraw-Hill Education (Asia). Permission required for reproduction or display.

*134 CONSERVATION OF MASS AND ENERGY EQUATIONSThe total energy of a liquid flowing in an open channel.Continuity Equation.

*ENERGY EQUATIONThe total energy of a liquid flowing in an open channel.The slope of the bottom of the channelIf the channel bottom is straight (the bottom slope is constant):This equation has the advantage that it is independent of the reference datume or elevation

*In the design of open-channel systems, the bottom slope is selected such that it provides adequate elevation drop to overcome the frictional head loss and thus to maintain flow at the desired rate. Therefore, there is a close connection between the head loss and the bottom slope, and it makes sense to express the head loss as a slope (or the tangent of an angle). This is done by defining a friction slope asThe total energy of a liquid at two sections of an open channel.Note that the friction slope is equal to the bottom slope when the head loss is equal to the elevation drop. That is, Sf = S0 when hL = z1 - z2.The energy line z + y + V2/2g (total mechanical energy of the liquid expressed as a head) above the horizontal reference datum. The energy line is typically sloped down like the channel itself as a result of frictional losses, the vertical drop being equal to the head loss hL and thus the slope being the same as the friction slope.

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