University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

379

Pages:

5
Author:

Jabin F.

Gradually Varied Flow The pressure distribution is assumed to be hydrostatic. The bed slope is very small. Channel is prismatic. The Energy correction factor α is unity. Resistance to flow is given by Manning's or Chezy's Eqn with slope taken as energy line slope. The Roughness coeff. is independent of depth of flow and is constant throughout the channel Reach considered. Differential Equation for GVF -> H = z + y + V^2 / 2g d/dy (1/A^2) = (-2/A^3) * (dA/dy) H = z + y + Q^2 / (A^2 * 2g) dH/dx = dz/dx + dy/dx + d/dx (Q^2 / (2gA^2)) -Sf = -So + dy/dx + d/dy (Q^2 / (2gA^2)) * dy/dx So - Sf = dy/dx + Q^2 / 2g * (-2/A^3 * dA/dy) * dy/dx So - Sf = (dy/dx) * (1 - (Q^2 / (gA^3)) * (dA/dy)) dA = Tdy dA/dy = T So - Sf = (dy/dx) * (1 - (Q^2 T) / (gA^3)) dy/dx = (So - Sf) / (1 - (Q^2 T) / (gA^3)) = (So - Sf) / (1 - Fr^2) H = E + Z dH/dx = dE/dx + dZ/dx -Sf = dE/dx - So dE/dx = So - Sf