(Solved): MATLAB Question Given for flow depth y, channel bottom \( b \) and flow rate \( Q \), Specific Ener ...

MATLAB Question

Given for flow depth y, channel bottom \( b \) and flow rate \( Q \), Specific Energy is defined as: \[ E=y+\frac{Q^{2}}{2 g b^{2} y^{2}} \ldots \ldots \text { (1) } \] where, \( g \) is gravity and in customary unit \( g=32.2 \mathrm{ft} / \mathrm{s}^{2} \). The equation gives the value of \( \mathrm{E} \) in length unit. So, in customary unit \( \mathrm{E} \) will have unit of \( \mathrm{ft} \). For a given \( Q \) and \( b, E \) values can be calculated for varying y value. For example, for a river channel with bottom width \( b=3 \mathrm{ft} \) and flow rate \( Q=5 \mathrm{cfs} \), when flow depth \( y=0.5 \mathrm{ft}, \mathrm{E} \) should be \( 0.6725 \mathrm{ft} \) and for \( y=1 \mathrm{ft}, E=1.043 \mathrm{ft} \). Find \( \mathrm{E} 1 \) for \( \mathrm{y}=[0.1: 0.1: 2], b=3 \mathrm{ft} \) and \( \mathrm{Q} 1=5 \mathrm{cfs} \) and find \( E 2 \) for \( y=[0.1: 0.1: 2], b=3 \mathrm{ft}, Q 2=10 \mathrm{cfs} \) Draw a figure (similar to the sample shown below) with a line showing E1 (along \( x \) axis) vs y (along y axis). In the same figure, show E2 vs y line. Also, show a line (the blue line in the sample figure) that passes through two points \( (0,0) \) and \( (2,2) \). Label the \( x \) axis as 'Specific Energy \( \mathrm{E}(\mathrm{ft})^{\prime} \) ' \( y \) axis as 'Flow depth \( y(\mathrm{ft}) \) using the above