Question

Water isflowing steadily in a 0.6-m wide rectangular open channel at a rate of 0.3 m3/s. If the depth is 0.15 m, a) determine i) the flow velocity, ii) hydraulic radius and iii) the specific energy. b) Is the flow subcritical or supercritical?

Answer 1

a) i)
`v = 3.333\,(m)/(s)`, ii)
`R_(h) = 0.06\,m`, iii)
`E_(s) = 0.716\,m`, b)
`Fr = 2.748` (Supercritical).

Step-by-step explanation:

a) i) The flow velocity of water is:

`v = (\dot V)/(w\cdot h)`

`v = (0.3\,(m^(3))/(s) )/((0.6\,m)\cdot (0.15\,m))`

`v = 3.333\,(m)/(s)`

ii) The hydraulic radius of the channel:

`R_(h) = (w\cdot h)/(2\cdot (w+h))`

`R_(h) = ((0.6\,m)\cdot (0.15\,m))/(2\cdot (0.6\,m+0.15\,m))`

`R_(h) = 0.06\,m`

iii) Let assume that height is equal to zero. Then, the specific energy is:

`E_(s) = 0.15\,m + ((3.333\,(m)/(s) )^(2))/(2\cdot (9.807\,(m)/(s) ))`

`E_(s) = 0.716\,m`

b) The characteristics of the flow in the open channel is inferred from the Froude number, whose formula is:

`Fr = (v)/(√(g\cdot h) )`

`Fr = \frac{3.333\,(m)/(s) }{\sqrt{(9.807\,(m)/(s^(2)) )\cdot (0.15\,m)} }`

`Fr = 2.748`

As
`Fr > 1`, then flow is supercritical.