Hydraulic Radius Calculator

About the Hydraulic Radius Calculator

The hydraulic radius is a fundamental geometric property used throughout fluid mechanics. Defined as the ratio of cross-sectional flow area to wetted perimeter (Rh = A/P), it characterizes how efficiently a channel shape conveys flow. The closely related hydraulic diameter Dh = 4A/P = 4Rh is used to substitute non-circular cross-sections into pipe-flow equations like Darcy–Weisbach and the Reynolds number.

For a full circular pipe, Rh = D/4 and Dh = D, which is why the hydraulic diameter collapses to the actual diameter. For non-circular ducts — rectangular, trapezoidal, annular — Dh provides the equivalent pipe diameter for friction and heat-transfer calculations. In open channels, the wetted perimeter excludes the free surface, so only the submerged walls count.

This calculator supports five cross-section types: circular (with partial fill), rectangular, trapezoidal, triangular, and custom (direct A and P entry). The fill-level feature for circular pipes is especially useful for sanitary sewer and stormwater design, where pipes rarely run full.

When This Page Helps

Hydraulic radius and diameter are needed for every pipe, duct, and channel calculation — from pressure-drop estimates in rectangular HVAC ducts to stormwater design in trapezoidal ditches. This calculator handles all common shapes and partial-fill conditions.

How to Use the Inputs

1. Select the cross-section shape from the dropdown.
2. Enter the dimensions — pipe diameter and fill %, or width/depth for open channels.
3. Use a pipe-size preset to quickly evaluate standard sizes.
4. Read the hydraulic radius (Rh) and hydraulic diameter (Dh) from the outputs.
5. Review the equivalent circular diameter for area-based comparisons.
6. For circular pipes, the variant table shows Rh at 25%, 50%, 75%, and 100% fill.

Example Calculation

Tips & Best Practices

• For sewer design, pipes typically run at 50–75% fill to leave headroom for surge flow.
• A half-full circular pipe has Rh = D/4 — same as a full pipe, which is a coincidence of geometry.
• For annular ducts, Dh = D_outer − D_inner (the gap width).
• Wide shallow channels are hydraulically efficient; deep narrow channels are not.
• Use the equivalent circular diameter to compare different shapes on an equal-area basis.

When To Use This Calculator

Calculate hydraulic radius Rh = A/P and hydraulic diameter Dh = 4A/P for circular, rectangular, trapezoidal, and triangular cross-sections. Use it when you need a repeatable calculation in the physics / fluid category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Frequently Asked Questions

• Why is the hydraulic diameter 4 times the hydraulic radius?

  The factor of 4 makes Dh equal to the actual diameter for a full circular pipe: D = 4 × (πD²/4)/(πD) = D. This convention simplifies substitution into standard pipe-flow equations.

• Does the free surface count in the wetted perimeter?

  No. The wetted perimeter includes only surfaces in contact with the fluid. In an open channel, the top (air–water interface) is excluded.

• What is the maximum hydraulic radius for a partially filled pipe?

  Interestingly, a circular pipe achieves its maximum Rh at about 81% fill — not at 100%. This is because the wetted perimeter grows faster than the area near the top of the circle.

• How is Dh used in the Reynolds number?

  For non-circular cross-sections, Re = ρVDh/μ, where Dh replaces the pipe diameter. This gives the same friction factor from the Moody chart (approximately).

• What shape gives the best hydraulic efficiency?

  For a given area, a semicircle has the least wetted perimeter and thus the highest Rh. Among practical shapes, a wide-and-shallow trapezoidal channel is more efficient than a deep-and-narrow one.

• Can I use hydraulic radius in Manning's equation?

  Yes — Manning's formula v = (1/n) Rh^(2/3) S^(1/2) uses the hydraulic radius directly. It is the standard method for open-channel flow calculations.