Open-channel hydraulics in worksheet tabs. Pick up where you left off or start something new from the sidebar.
FlowStudio is an open-channel hydraulics workspace. You organize worksheets (solvers for channels, weirs, and more) inside projects, then open them as tabs in the main area.
Worksheets use SI units with \(g = 9.80665\,\mathrm{m/s^2}\). Formulas below match the implementations in the solvers (Manning, gradually varied flow, weirs, etc.).
Uniform flow (Manning): discharge \(Q\), area \(A\), hydraulic radius \(R = A/P\), bed slope \(S > 0\) downstream, Manning \(n\).
$$ Q = \frac{1}{n}\, A\, R^{2/3}\, S^{1/2}, \qquad A = by,\quad P = b + 2y,\quad R = \frac{A}{P} $$Hydraulic depth and Froude number for a wide rectangle use \(D_h = A/T = y\), \(T = b\):
$$ \mathrm{Fr} = \frac{V}{\sqrt{g D_h}}, \qquad V = \frac{Q}{A} $$Bottom width \(b\), side slope \(z{:}1\) (H:V). Same Manning uniform flow as above with
$$ A = y(b + zy), \qquad P = b + 2y\sqrt{1+z^2}, \qquad T = b + 2zy, \qquad D_h = \frac{A}{T} $$Diameter \(D\), radius \(R=D/2\), depth \(y\) from invert. Wetted area and wetted angle \(\theta\) from geometry (circular segment):
$$ \cos\theta = \frac{R-y}{R}, \qquad A = R^2\left(\theta - \frac{\sin 2\theta}{2}\right), \qquad P = 2R\theta $$ $$ T = 2R\sin\theta, \qquad D_h = \frac{A}{T}, \qquad Q = \frac{1}{n} A R_h^{2/3} S^{1/2},\quad R_h=\frac{A}{P} $$User-defined cross-section polyline \((x,z)\). For water surface at elevation \(W = z_{\mathrm{inv}} + y\), the solver builds the wetted chain, then integrates trapezoids for \(A\) and segments for \(P\). Top width \(T\) follows from surface intersections. Uniform flow uses the same Manning relation with \(R = A/P\).
$$ Q = \frac{1}{n}\, A\, R^{2/3}\, S^{1/2}, \qquad \mathrm{Fr} = \frac{V}{\sqrt{g D_h}},\quad D_h = \frac{A}{T} $$Prismatic channel; one-dimensional gradually varied flow with Manning friction slope \(S_f\) and bed slope \(S_0\):
$$ \frac{dy}{dx} = \frac{S_0 - S_f}{1 - \mathrm{Fr}^2}, \qquad S_f = \frac{n^2 V^2}{R^{4/3}} $$Standard step option uses fixed \(\Delta y\) with \(\Delta x \approx \Delta y / (dy/dx)\). Integration pauses when \(|1-\mathrm{Fr}^2|\) is very small (near critical). For a rectangle, \(y_c\) from unit discharge \(q=Q/b\) is
$$ y_c = \left(\frac{q^2}{g}\right)^{1/3} $$For a trapezoid, critical depth solves \(\mathrm{Fr}^2 = Q^2 T/(g A^3) = 1\) (implemented numerically).
Contracted depth \(y_2 = C_c a\), unit discharge \(q=Q/b\). Specific energy at the vena contracta and upstream pool depth \(y_1\) from energy matching (with normal-depth constraints as coded).
$$ E = y + \frac{q^2}{2g y^2} $$Downstream, supercritical GVF may meet a hydraulic jump to subcritical tailwater \(y_t\). For a wide rectangular channel, Belanger (momentum) gives the sequent depth from supercritical \(y'\):
$$ \frac{y''}{y'} = \frac{1}{2}\left(\sqrt{1 + 8\,\mathrm{Fr}'^2} - 1\right), \qquad \mathrm{Fr}' = \frac{V'}{\sqrt{gy'}} = \frac{q}{y'\sqrt{gy'}} $$The sheet locates the jump where the M3 profile reaches the supercritical depth whose sequent is \(y_t\), then continues subcritical GVF. Submerged jumps at the gate are flagged, not fully modeled.
Suppressed thin-plate weir, crest length \(L\), head \(H\) above crest, user coefficient \(C_d\):
$$ Q = \frac{2}{3}\, C_d\, L\, \sqrt{2g}\, H^{3/2} $$Trapezoidal notch with side slope \(1{:}4\) (H:V) so end contractions are nominally compensated; the same head–discharge relation is used with crest length \(L\) and an adjustable \(C_d\) for your standard or calibration.
$$ Q = \frac{2}{3}\, C_d\, L\, \sqrt{2g}\, H^{3/2} $$When signed in, use the folder button on a project to add folders, then drag worksheets onto a project or folder to organize them. Folders are stored on the server.
Use Profile in the title bar to see your account details. Use Account to sign in or out. While signed out, worksheets can still be saved in this browser only.
Click the projects icon in the activity bar to return to your tree. Leave this guide open as a tab, or close it with × on the tab. The Theory by worksheet section above lists the main equations used by each solver type.
FlowStudio
Open-channel hydraulics workspace
FlowStudio helps you run and organize hydraulic calculations—open channels, weirs, and related worksheets—inside projects you can sync when you sign in.
Alex Academia
Made for engineers, students, and anyone working with open-channel flow. Solver implementations and UI evolve with the product; see the Guide in this menu for how to use the app.
FlowStudio · 2026