Resolve example 5.3.1 for a channel bed slope of 0.003.EXAMPLE 5.3.1Consider a vertical sl...

Resolve example 5.3.1 for a channel bed slope of 0.003.

EXAMPLE 5.3.1

Consider a vertical sluice gate in a wide rectangular channel (R = A/P = By/(B + 2Y) ≈ y because B ≫ 2y). The flow downstream of a sluice gate is basically a jet that possesses a vena contracta (see Figure 5.3.2). The distance from the sluice gate to the vena contracta as a rule is approximated as the same as the sluice gate opening (Chow, 1959). The coefficients of contraction for vertical sluice gates are approximately 0.6, ranging from 0.598 to 0.611 (Henderson, 1966). The objective of this problem is to determine the distance from the vena contracta to a point b downstream where the depth of flow is known to be 0.5 m deep. The depth of flow at the vena contracta is 0.457 m for a flow rate of 4.646 m3/s per meter of width. The channel bed slope is 0.0003 and Manning’s roughness factor is n = 0.020.

SOLUTION

To compute the distance, Δx from ya to yb, the gradually varied flow equation (5.3.1) can be used,

where Δy = y2 − y1. Solving for Δx, we get

The friction slope is computed using Manning’s equation (5.1.22) with average values of the hydraulic radius

so

Let us use the following values for this example:

Now we get

The distance from a to b, Δx, is

The distance from the sluice gate to b is .

Figure 5.3.2 Flow downstream of a sluice gate in a wide rectangular channel.