A rectangular channel has a bottom width of of 2 m and longitudinal slope of the channel is 0.0003. What will be the average shear stress on the channel boundary when the flow takes place at a uniform depth of 1.25 m? (Take γ = 10 kN/m3)

Question

Question

This question was previously asked in

BPSC AE Paper 6 (Civil) 14 Oct 2022 Official Paper

Answer 1

Concept:

The average shear stress on the channel boundary in open channel flow can be determined using the formula:

$τ_{0} = γ R S$

Where:

Calculation:

Given:

1. Calculate the Cross-Sectional Area ( $A$ ) of the Flow:

$A = b \times y$

$A = 2 \times 1.25$

$A = 2.5 m^{2}$

2. Calculate the Wetted Perimeter ( $P$ ) of the Channel:

$P = b + 2 y$

$P = 2 + 2 \times 1.25$

$P = 4.5 m$

3. Calculate the Hydraulic Radius ( $R$ ):

$R = \frac{A}{P}$

$R = \frac{2.5}{4.5}$

$R = 0.5556 m$

4. Calculate the Shear Stress ( $τ_{0}$ ):

$τ_{0} = γ R S$

$τ_{0} = 10 \times 0.5556 \times 0.0003$

$τ_{0} = 0.0016668 {kN/m}^{2}$

$τ_{0} = 1.6668 {N/m}^{2} \approx 1.67 {N/m}^{2}$