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### Flow over Channel Rise Hump Formula

Flow over Channel Rise Hump Formula

In the case of flow in a constant width (b) horizontal rectangular channel with a small rise on the floor (Figure 1),

Figure 1, Open-channel flow over a rise.

the relations are:

Eq. 1

* V _{1}^{2} / 2 + g h_{1} = V_{2}^{2} / 2 + g ( h_{2} δ )*

Eq. 2

Q = V_{1} b h_{1} = V_{2} b h_{2}

Q^{2} / ( 2 g b^{2} h_{1}^{2} ) = h_{1} Q^{2} / ( 2 g b^{2} h_{2}^{2} ) + ( h_{2} + δ )

Note that the sum of the two terms h + Q^{2} / ( 2 g b^{2} h_{2}^{2} ) is
called the specific head, H. The critical specific head H, and
the critical depth h, can be found by taking the derivative
of above term and equating it to zero.

h_{c}^{3} = Q^{2} / ( g b^{2} )

H_{c} = 3 h_{c} / 2

Note that for a given specific head and flow rate, two different depths of h are possible. The Froude n d e r V/(gh) specifies the flow characteristics of the channel flow. If it is less than unity, it is called subcritical, or tranquil, flow. If it is more than unity, it is called supercritical, or rapid, flow.

Where:

Q = flow, ( ft^{3} / sec, m^{3} / sec)

V_{1} = flow velocity, (ft / sec, m / sec)

V_{2} = flow velocity, (ft / sec, m / sec)

g = Gravity (32.2 ft/sec^{2} , 9.81 m/sec^{2} )

b = channel width, (ft, m)

h_{1} = height, (ft, m)

h_{2} = height, (ft, m)

δ = rise, (ft, m)

H_{c} = critical specific head, (ft, m)

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Reference:

Rules of Thumb for Mechanical Engineers

J. Edward Pope, Editor