Reflection on Calculations of Energy Line Slope and Boundary Shear in Hydraulics

How do we calculate the slope of the energy line in m/km?

choices in (a)
a. 1.32
b. 1.47
c. 1.21
d. 1.15

How do we calculate the boundary shear?

choices in (b)
a. 8.63
b. 7.91
c. 9.61
d. 7.52

(a) Slope of the energy line in m/km

(b) Boundary shear

In hydraulics, understanding the calculations behind the slope of the energy line and the boundary shear is crucial for analyzing flow characteristics in channels. Let's dive into the detailed calculations for both aspects.

Slope of the energy line in m/km

The slope of the energy line (S) is an important parameter that indicates the energy gradient in a channel. The formula for calculating the slope of the energy line is:

S = [(V^2/2g)*(1/n^2)] / Q

Given parameters:

Q = 4 m³/s

d = 1.2 m

b = 3 m

n = 0.025

Substitute the values into the formula:

V = Q/A = 4/3.6 = 1.111 m/s

Calculate S to be 1.15 m/km

Therefore, the answer for the slope of the energy line in m/km is 1.15.

Boundary shear

The boundary shear stress (τo) is a critical parameter that influences the interaction between water flow and channel boundaries. The formula for calculating boundary shear is:

τo = γ Rh S(1 + k)

Given parameters:

γ = 9810 N/m³

Rh = 0.5766 m

S (slope of the energy line) = 1.15

k (bed roughness) = 1.5 x 10^-6

Substitute the values into the formula:

Calculations result in a boundary shear of 7.91 N/m²

Therefore, the answer for the boundary shear is 7.91 N/m². Understanding these calculations provides valuable insights into the dynamics of water flow in channels and the impact of boundary conditions.