Calculate discharge (flow rate) as Q = A × v from flow area and mean velocity, or from orifice head and a discharge coefficient, in L/s, m³/s, gpm or cfs.
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Discharge Formulas
The core relationship for volumetric discharge in fluid mechanics is Q = V x A, where Q is the volume flow rate, V is the mean fluid velocity, and A is the cross-sectional area perpendicular to flow. This equation applies to any conduit geometry as long as V represents the area-averaged velocity.
For a simple incompressible reservoir-orifice model, Q = Cd x A x sqrt(2gH), where Cd corrects theoretical flow for contraction and other effects, g is standard gravity 9.80665 m/s², and H is the driving head. This calculator’s head mode assumes free discharge with negligible approach velocity. Submerged outlets require a head difference; pressurized-pipe meters require the applicable calibrated relationship. Cd is typically below one in this simple free-orifice model. Measured area-averaged velocity already includes actual flow effects, so its mode uses Q = A x v without applying Cd again. The separate reference-velocity mode retains Q = Cd x A x v when v is the uncorrected reference velocity.
For rectangular weirs under the applicable free-nappe and head-to-crest-length conditions, the Francis approximation is Q = 1.84 x L x H^1.5 with L and H in metres and Q in m³/s. Replacing L with L − 0.2H represents two end contractions. For a standard fully contracted 90-degree V-notch, the Cone equation is Q = 2.49 x H^2.48 with H in feet and Q in ft³/s; USBR describes a range of about 0.05–4.25 ft³/s subject to installation limits. The Kindsvater–Shen method is a different effective-head and angle formulation. These weir relationships are background information, not calculator modes.
In electrical contexts, average current is I = Q/t, where I is in amperes, Q is charge in coulombs, and t is elapsed time in seconds. Electrical charge discharge is separate from the volumetric flow calculated here.
Discharge Coefficient Reference Values
The discharge coefficient (Cd) relates actual flow to a specified theoretical model. It depends on geometry, head definition, Reynolds number and calibration. The following nominal reservoir-orifice examples from EPA are illustrative, not coefficients for every device or installation.
| Device | Nominal Cd | Scope |
|---|---|---|
| Sharp-edged opening | 0.61 | Nominal sharp opening |
| Rounded opening | 0.98 | Nominal rounded inlet |
| Short tube | 0.80 | Nominal short-tube example |
| Borda inlet | 0.51 | Nominal re-entrant inlet |
Cd near 0.6 means actual flow is about 60% of the flow predicted by the specified theoretical model. The coefficient combines contraction and velocity effects; it is not itself an energy-loss coefficient. Use a geometry-specific calibration rather than inferring total energy loss from Cd alone.
Manning’s Roughness Coefficients
In SI units, the Manning uniform-flow approximation is Q = (1/n) x A x R^(2/3) x S^(1/2), with Q in m³/s, area A in m², hydraulic radius R = A / wetted perimeter in metres, and energy slope S dimensionless. US customary units use an approximately 1.486 multiplier. Flow varies inversely with n when the other inputs remain fixed. The following EPA SWMM reference ranges describe specific conditions and do not replace site calibration; Manning discharge is not a calculator mode here.
| Material or condition | n (low) | n (high) |
|---|---|---|
| Trowelled concrete | 0.011 | 0.015 |
| Unfinished concrete | 0.014 | 0.020 |
| Uncoated iron conduit | 0.011 | 0.016 |
| Corrugated storm drain | 0.021 | 0.030 |
| Straight weathered excavation | 0.018 | 0.025 |
| Uniform clean gravel channel | 0.022 | 0.030 |
| Winding earth, grass/some weeds | 0.025 | 0.033 |
| Straight clear stream, no deep pools | 0.025 | 0.033 |
| Clear winding reach, pools/shoals | 0.033 | 0.045 |
| Scattered brush/heavy weeds | 0.035 | 0.070 |
| Heavy timber, water below branches | 0.080 | 0.120 |
Surface condition, vegetation, channel geometry and flow depth affect the appropriate roughness coefficient. Compare values for matching conditions and hold area, hydraulic radius and slope fixed when evaluating the effect of n alone.
Types of Discharge Measurement
Discharge is expressed as volumetric (Q, in m³/s), mass (Qm = rho x Q, in kg/s), or weight (Qw = gamma x Q, in N/s). Mass discharge is essential when density varies with temperature or pressure.
Orifice plates and Venturi meters use calibrated differential-head relationships for pressurized flows. Weirs and flumes can derive open-channel discharge from water levels under their calibrated geometry, installation and flow conditions.
Discharge in Hydrology
USGS streamgages use stage-discharge ratings to support flow monitoring, flood forecasting and water management. Bankfull-flow recurrence varies by region and channel; 1.5–2 years is a common approximation, not a universal rule. Discharge measurements also support pollutant-load calculations and applicable permit requirements.
Unit Conversions
| From | To | Factor |
|---|---|---|
| m3/s | cfs | 35.3147 |
| m3/s | L/s | 1000 |
| m3/s | US gal/min | 15850.3 |
| cfs | US gal/min | 448.831 |
| cfs | acre-ft/day | 1.9835 |
| L/s | US gal/min | 15.8503 |
| m3/s | megalitres/day | 86.4 |
One cfs flowing 24 hours delivers ~1.98 acre-feet. A 100 acre-feet/year water right equals about 0.138 cfs continuous diversion.
FAQ
Discharge (Q) is volume of fluid passing a cross-section per unit time: Q = V x A. Units are m3/s or cfs. Can be expressed as mass flow (kg/s) by multiplying by density.
For a simple reservoir-orifice model, Cd is typically below one and relates actual flow to the specified theoretical flow. Contraction and velocity effects both matter. Use a coefficient appropriate to the geometry, driving head and calibration.
Weirs rate open-channel flow using water level and a suitable calibrated geometry. Orifices and pipe meters need the applicable opening, head definition and flow relationship.
With area, hydraulic radius and energy slope fixed, Manning discharge varies inversely with n. Doubling n halves the modeled flow. Choose roughness for the actual material and channel condition.
