Hydraulic Depth Calculator
Calculate hydraulic depth (mean depth) and analyze flow regime for open channels and partially filled pipes
Dh = A / T | Visualizing your selected channel type
📚 Understanding Hydraulic Depth in Open Channel Flow
Hydraulic depth (also called mean depth) is one of the most important dimensionless parameters in open channel hydraulics. It's essential for analyzing flow regimes, predicting hydraulic jumps, designing channel transitions, and understanding the fundamental behavior of water flowing in open channels and partially filled pipes.
What is Hydraulic Depth?
Hydraulic depth (Dh) is defined as the ratio of the flow cross-sectional area to the top water surface width: Dh = A/T. It represents the average vertical distance that water molecules travel to reach the water surface. For rectangular channels, hydraulic depth equals the actual depth (y). For non-rectangular shapes, Dh is less than actual depth because the top width is greater than an equivalent rectangle would be.
Hydraulic Depth vs. Actual Depth
Actual depth (y) is the measured vertical distance from the channel bottom to the water surface. Hydraulic depth (Dh) relates flow area to top width. These are equal only in rectangular channels. In trapezoidal channels with sloping sides, the top width is wider than the bottom, so Dh < y. In triangular channels, Dh = y/2. This distinction is critical for accurate hydraulic analysis.
The Froude Number and Flow Regime Analysis
The Froude number (Fr = v/√(g × Dh)) is the most important dimensionless parameter for open channel flow. It compares inertial forces (tendency of flow to continue) with gravitational forces (restoring force). A Froude number less than 1 indicates subcritical flow (slow, smooth, controlled). Fr = 1 represents critical flow (exact balance of forces). Fr > 1 indicates supercritical flow (fast, rough, unstable). Hydraulic depth is critical in this calculation—larger Dh increases the denominator, reducing Fr.
How Channel Shape Affects Hydraulic Depth
Rectangular Channels: Dh = y (actual depth). Simple but not self-cleaning for sediment transport.
Trapezoidal Channels: Dh < y because sloping sides increase top width. Most common in irrigation and drainage systems. Better stability than rectangular channels.
Triangular Channels: Dh = y/2 (smallest hydraulic depth for the same actual depth). Rarely used alone but important in composite channels.
Circular Pipes (Partially Filled): Dh is smallest at very low depths, increases to maximum (D/4) when full. Dh is always less than actual depth for partially filled pipes.
Critical Depth and Energy Considerations
Critical depth (yc) is the depth at which Froude number equals 1. At critical depth, the specific energy of the flow is minimum for a given discharge. Below critical depth, supercritical flow dominates (Fr > 1). Above critical depth, subcritical flow occurs (Fr < 1). Critical depth depends on channel shape and flow rate. Engineers use critical depth to design efficient channel transitions, spillways, and control structures.
Practical Applications of Hydraulic Depth
| Application | Why Hydraulic Depth Matters | Key Design Consideration |
|---|---|---|
| Open Channel Design | Determines Manning's equation result and flow velocity | Optimal channel shape for target velocity |
| Hydraulic Jumps | Controls where jumps occur and jump height | Transitioning from supercritical to subcritical |
| Weir Design | Affects discharge coefficient and accuracy | Critical depth in approach flow |
| Channel Transitions | Predicts rise or drop in water surface | Avoiding supercritical transitions |
| Sewer Analysis | Determines efficiency of partially filled pipes | Optimizing for depth of flow |
| Flood Control | Analyzes flow behavior at high discharges | Predicting supercritical conditions |
Why Engineers Use Hydraulic Depth Instead of Actual Depth
Hydraulic depth accounts for the actual geometry of the channel. In Manning's equation and other empirical relationships, hydraulic depth provides more accurate predictions of velocity and energy dissipation. For non-rectangular channels, using actual depth leads to significant errors. Hydraulic depth is the "effective" depth that determines how water molecules interact with the channel boundary and gravity.
❓ Frequently Asked Questions
Hydraulic depth (Dh), also called mean depth, is defined as: Dh = A/T, where A is the flow cross-sectional area and T is the top water surface width. It represents the average vertical distance from the channel bottom to the water surface. For rectangular channels, Dh equals actual depth (y). For non-rectangular shapes like trapezoidal or triangular channels, Dh is less than actual depth because the top width is greater than the bottom width.
Actual depth (y) is the measured vertical distance from the channel bottom to the water surface—what you observe in the field. Hydraulic depth (Dh) is the ratio A/T, which accounts for the channel geometry. They are equal only in rectangular channels. In trapezoidal channels, the sloping sides make the top width wider than the bottom, so Dh < y. In triangular channels, Dh = y/2. This distinction is critical: equations and predictions based on actual depth alone would be inaccurate for non-rectangular channels.
The Froude number (Fr = v/√(g × Dh)) is a dimensionless number predicting open channel flow regime. Fr < 1: subcritical flow (slow, smooth, controlled by downstream conditions). Fr = 1: critical flow (exact balance of forces). Fr > 1: supercritical flow (fast, rough, controlled by upstream conditions). Hydraulic depth is critical in this formula—larger Dh decreases Froude number. Understanding Fr is essential for predicting hydraulic jumps, designing efficient channels, and analyzing stability.
Channel shape dramatically affects hydraulic depth. Rectangular channels (Dh = y) are simplest but require side protection. Trapezoidal channels are most common (Dh < y due to wider top width)—they're stable and self-cleaning. Triangular channels have smallest Dh (=y/2) but are rarely used alone. Circular pipes vary: smallest Dh at low depths, maximum (D/4) when full. Engineers choose shapes based on stability, self-cleaning requirements, and efficiency—all influenced by how hydraulic depth behaves.
Critical depth (yc) is the depth at which Froude number equals 1, where specific energy is minimum for a given discharge. At critical depth, hydraulic depth equals the corresponding value for Fr = 1. Critical depth is fundamental to channel design: below it, supercritical flow dominates (Fr > 1, flows controlled upstream). Above it, subcritical flow occurs (Fr < 1, flows controlled downstream). Transitions between these regimes create hydraulic jumps. Critical depth depends on both channel geometry and flow rate.
Hydraulic depth is essential for: (1) Manning's equation calculations (larger Dh increases velocity), (2) Froude number analysis to predict flow regime, (3) specific energy calculations for channel design optimization, (4) critical depth determination, (5) hydraulic jump position prediction, (6) weir discharge coefficient calculations, (7) channel transition design. Engineers use Dh to select efficient shapes, optimize depths, and ensure stable flow conditions across design scenarios.
In partially filled circular pipes, hydraulic depth is smallest at very shallow depths (small area, large perimeter—poor efficiency). As depth increases, Dh increases because area grows faster than perimeter. Maximum Dh occurs at full pipe (Dh = D/4). At half-depth (y = D/2), Dh is about 0.18×D (less than half of full-pipe value). This non-linear relationship is why sewers are designed to flow under pressure at full capacity when possible—it provides maximum hydraulic efficiency.