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Open Channel Flow Gradually Varied Flow (Cont)

Example: (continued)

To remain on the specific energy diagram for q = 6 ft²/sec and achieve critical conditions imagine inserting an artificial bump in the floor of the channel as shown below to reach

critical flow at the highest point on the artificial bump.

The energy equation between stations 1 and c is y₁ + V₁²/2g + z₁ = y_c + V_c²/2g + z_c

Or (since z₁ = 0) y₁ + V₁²/2g = y_c + V_c²/2g + z_c and E₁ = E_c + z_c

From the specific energy diagram, E_c = E_min = 1.56 ft.

Thus with a bump of height z_c = E₁ - E_c = 2.59 – 1.56 = 1.03 ft the flow could

then reach supercritical flow where F_r> 1 and thus the downstream elevation

of the free surface, y_2b, with the bump (and critical flow at the apex of the bump)

is y_2b = 0.55 ft as shown on the specific energy diagram.

Click here to move on to a discussion of rapidly varying flow (hydraulic jump).

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