Broad Crested Weir Calculator — Open Channel Flow Rate with Q = C·L·H^(3/2)

Broad Crested Weir Calculator

The broad crested weir calculator helps you determine the upstream flow rate over a weir in an open channel flow. A weir is a barrier installed over rivers or outlets of reservoirs, lakes, and ponds to control the water flow and the height of the water level. It is also known as a low-level dam that helps prevent flooding, monitor water levels, perform flow analysis, and measure the volumetric flow rate of streams.

Weirs come in different types based on the barrier's geometry, such as sharp-crested, broad-crested, narrow-crested, and Ogee-shaped. You can also classify weirs based on the shape of the opening, i.e., rectangular, triangular, and trapezoidal. This calculator focuses on the broad-crested weir. Read on to understand the broad crested weir equation and how to perform weir flow calculations.

What is a broad-crested weir?

When the upstream head above the crest is between 5% and 50% of the crest length, the weir acts as a broad-crested weir. This definition depends on the upstream head because, if the approaching head is large, a thick weir can behave like a sharp-crested weir instead.

Broad-crested weirs are usually rectangular in shape and are most suitable for larger flows. The water follows the surface of the structure and flows like a waterfall after crossing the weir. Over the crest, the flow passes through critical depth, which is what makes the discharge predictable from the head alone.

Broad-crested weir equation

The weir flow rate is a function of the coefficient of discharge (C_d), the upstream head (H), and the length (width) of the weir (L). The broad crested weir equation to calculate the discharge (Q) is:

Q = C × L × H^3/2

The broad-crested weir coefficient C depends on the coefficient of discharge C_d and the acceleration due to gravity g, such that:

C = C_d × (2/3)^3/2 × √g

where:

• Q — discharge (volumetric flow rate) over the weir;
• C — broad-crested weir coefficient (depends on the unit system, because it contains √g);
• C_d — coefficient of discharge (dimensionless, typically 0.85–1.0 for broad-crested weirs);
• L — length (width) of the weir across the channel;
• H — upstream head of water above the crest; and
• g — acceleration due to gravity (9.80665 m/s² or 32.174 ft/s²).

Combining both expressions gives the full form used in the calculator:

Q = C_d × (2/3)^3/2 × √g × L × H^3/2

Using the broad crested weir calculator

1. Choose your unit system — metric (SI) or American (imperial).
2. Enter the coefficient of discharge C_d (use ≈ 0.95 if you are unsure).
3. Enter the length (width) of the weir L in metres or feet.
4. Enter the upstream head H above the crest in metres or feet.
5. The calculator returns the discharge Q in m³/s, ft³/s, L/s and US GPM, plus the weir coefficient C and the discharge per unit width q = Q/L.

Example: Using the broad crested weir calculator

Suppose a rectangular broad-crested weir is 3 m wide, with an upstream head of 0.5 m and a coefficient of discharge of 0.95.

• Weir coefficient: C = 0.95 × (2/3)^1.5 × √9.80665 = 0.95 × 0.5443 × 3.1316 ≈ 1.619
• Discharge: Q = 1.619 × 3 × 0.5^1.5 = 1.619 × 3 × 0.3536 ≈ 1.718 m³/s (≈ 60.7 ft³/s)

FAQs

What is the difference between a broad-crested and a sharp-crested weir?

The difference lies in the crest length in the direction of flow. A broad-crested weir has a thick crest over which the flow reaches critical depth, so the head above the crest is roughly 5–50% of the crest length. A sharp-crested weir has a thin edge, and the nappe springs clear of the crest.

What is a typical coefficient of discharge for a broad-crested weir?

For a well-designed rectangular broad-crested weir, the coefficient of discharge C_d is usually about 0.85 to 1.0. Rounded upstream edges and a smooth crest push C_d towards the upper end of that range.

Why does the head appear to the power of 3/2?

Over a broad-crested weir the flow passes through critical depth, where the discharge per unit width is proportional to H^3/2. This comes from combining the critical-flow condition with the energy equation, which is why the broad-crested weir equation always uses an exponent of 1.5 on the head.

Does the unit system change the result?

The physical discharge is the same, but the numbers and the weir coefficient C differ because C contains √g, which has different values in metric and imperial units. This calculator computes everything internally in SI and reports the discharge in m³/s, ft³/s, L/s and US GPM so you can read it in whichever unit you need.