Question

A trapezoidal channel with base of 6 m and side slope of two horizontal to one vertical conveys water at 17 m³/sec with a depth of 1.5 m. The flow situation in the channel is:
1. Critical
2. Supercritical
3. Subcritical
4. None of the above

Answer 1

Correct Answer - Option 3 : Subcritical

Concept:

The Froude number is given by,

\({{\rm{F}}_{\rm{r}}}{\rm{ = }}\frac{{\rm{V}}}{{\sqrt {{\rm{gD}}} }}\)

Where,

V = Velocity of water, D = Y = Hydraulic depth = A/T

T = Top width of the channel

F_r = 1 → Critical flow

F_r < 1 → Subcritical flow or Tranquil flow

F_r > 1 → Supercritical flow or Shooting or Torrential flow

Calculation:

Given: Q = 17 m3/sec, Y = 1.5 m, B = 6 m

A = (1/2) × (6 + 12) × 1.5 = 13.5 m²

\({{\rm{F}}_{\rm{r}}}{\rm{ = }}\frac{{\rm{V}}}{{\sqrt {{\rm{gD}}} }}\)

Where,

V = Q/A, D = A/T

\(∴ {{\rm{F}}_{\rm{r}}}^2{\rm{ = }}\frac{{\rm{Q^2T}}}{{{{\rm{gA^3}}} }}\)

\(∴ {{\rm{F}}_{\rm{r}}}^2{\rm{ = }}\frac{{\rm{{(17)}^2× 12}}}{{{{\rm{9.81× {(13.5)}^3}}} }}=0.1436\)

∴ F_r = 0.379 < 1

Hence the flow is Subcritical