Siphon Hydraulic Calculation

Inverted-siphon head loss (Chezy friction + local), designed velocity and flow-capacity check.

1. Initial pipe diameter

Friction uses Chezy C=R^(1/6)/n, λ=8g/C²; local factors include inlet, gate slot, trash rack, bend, bypass, outlet and vent; then verify capacity and minimum velocity.

Design flow Q (m³/s)

Min flow Qmin (m³/s)

Siphon length L (m)

Roughness n

Initial velocity v' (m/s)

Chosen diameter D (m)

Initial area w'

—

m²

Initial diameter D'

—

Design velocity v

—

m/s

Flow area w

—

m²

2. Head loss 2.1 Friction loss

Hydraulic radius R

Chezy C

λ = 8g/C²

Hydraulic radius R

—

Chezy C

—

Friction loss hf

—

2.2 Local loss

Inlet ζ

Gate slot ζ

Rack bar thickness s

Rack spacing b

Rack angle a (°)

Bar shape factor β

Bend ζ

Bypass ζ

Channel area w渠

Outlet ζ

Vent ζ

Rack ζ

—

Total local ζ Σζj

—

Local loss hj

—

2.3 Total & allowable

Allowable head loss (m)

Total head loss z

—

Allowable − z

—

3. Flow capacity check

Checked capacity Q

—

m³/s

Min velocity vmin

—

m/s

Friction loss hf = λ·L·v²/(4R·2g) with R=D/4, C=R^(1/6)/n, λ=8g/C² (g=9.81); local loss hj = Σζj·v²/(2g). Checked capacity Q = w·(2gz)^0.5/(λL/D+Σζj)^0.5; min velocity vmin = Qmin/w should exceed 1.2 m/s.