The flow through a rectangular channel (width in x and height in z) is nonuniform with a velocity  profile of V(z) = mz+b. The velocity at the floor of the channel is V(z=0) and the velocity at the  top of the channel is V(z=Z).   a) Develop an expression for flow rate and average velocity using the given constants.  If the channel is 5m wide in x and 3m tall in z and V(z=0) = 0 m/s and V(z=3m) = 6 m/s:  b) Determine the value of the constants m and b in the velocity profile  c) Determine the value of the flowrate and average velocity of water in the channel.

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Q: 3 m P Lower reservoir 100 m 1 m Upper reservoir 10 m

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Open Channel Flow

Open channel flow is a branch of fluid mechanics. It deals with the flow of fluid in an open conduit or free surface. In an open channel flow, gravity induces the flow of water whose surface is open to the air. This flow is free-falling rather than confined in rigid body conduits. The open channel flow depends upon two parameters that are the cross-section of the conduit and the velocity profile. Practical examples of open channel flow are streams, rivers, canals, and other drainage systems.In open channel flow, the cross-sectional area of at least one of the sides is exposed to air, and the surface of water faces atmospheric pressure. This flow is also known as free gravity flow. The cross-sectional area of the conduit can be either man-made or a natural channel. For instance, the flow in rivers and streams are natural conduits, and the flow in a canal and sanitary systems are man-made or engineered channels.