---
title: "Detailed Bed Shear Equations"
canonical: "https://help.innovyze.com/space/xps/19662816/Detailed%20Bed%20Shear%20Equations"
format: markdown
---
The TUFLOW Bed Shear Equations are given as: 

***Metric Units: ***

![image](media://690a469c-9b10-47d8-a094-4c7e437d5c7a)

where:

> Macro (inline-media-image)

 = Density

> Macro (inline-media-image)

 = Gravity

> Macro (inline-media-image)

 = Velocity

> Macro (inline-media-image)

 = Manning's n

> Macro (inline-media-image)

 = Depth

Units are in N/m<sup>2</sup>

**In US Customary Units, the total bed shear stress is given as: **

![image](media://3716a5f8-118f-4f90-98e4-84f18fb7f9a7)

Where:

 > Macro (inline-media-image)

 = Specific weight of water

**R = **Hydraulic Radius

**S **= Energy Slope

**Manning's Energy Grade Line Slope in English Units is given as: **

![image](media://e1e19ddf-1451-4ad0-bed8-879288ec1a80)

Where: 

> Macro (inline-media-image)

 = Specific weight of water

**R** = Hydraulic Radius

**S** = Energy Slope

**CME** =1.486 in English units and 1.0 in SI units

![image](media://4be923f7-b3de-458c-be6f-669e6412b7d6)

Where: 

> Macro (inline-media-image)

 = Density

> Macro (inline-media-image)

 = Gravity

In channels where the width is 10 times greater than Depth (**R**), then (**R**) is taken is Depth (> Macro (inline-media-image)

).

With substitution, we get: 

![image](media://dc82bcd1-decf-41d5-8384-db43e35f0416)


With cancellation and roundup, we get: 

![image](media://c6e36b45-8b5b-4c8c-b921-aa91a1f24cb7)

Units are in **lb/ft**<sup>2</sup>