---
title: "Ackers-White (1973) Total Load Equation | Sediment Transport"
slug: "ackers-white-1973-total-load-equation"
description: "Read about Ackers-White (1973) total load equation."
tags: ["1D river modelling"]
updated: 2022-08-21T17:22:26Z
published: 2022-08-21T17:22:26Z
canonical: "help.floodmodeller.com/ackers-white-1973-total-load-equation"
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---

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# Ackers-White (1973) Total Load Equation

The Ackers-White equation was developed by determining the appropriate form of the equation from physical considerations and dimensional analysis, but using empirical data to determine the various coefficients. Both the original and the updated versions of the coefficients are available in the model. The calculation procedure for the Ackers-White equation is described below .

1. Determine the dimensionless sediment diameter, Dgr

![image.png](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackerimage020.gif) (4)

Where

D = particle diameter (Ackers and White advise the use of the Dsize) g = acceleration due to gravity s = specific gravity of sediment v = kinematic viscosity of water

1. Determine the transition exponent, n, the initial motion parameter, A, and the coefficient and exponent in the sediment transport function (c and M respectively)
2. Determine the volumetric sediment transport rate, G,

| For Dgr >60, | n = 0 |
| --- | --- |
|  | A = 0.17 |
|  | M = 1.5 |
|  | c = 0.025 |
| For 1 £ Dgr £ 60, | ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackerimage022.gif) |
|  | ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackersimage024.gif) |
|  | ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackersimage026.gif) |
|  | ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackersimage028.gif) |
3. Determine the particle mobility,

![image.png](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackersimage030.gif) (5)

Where

V* = shear velocity (= (g h S)0.5) V = mean flow velocity h = depth of flow

1. Determine the dimensionless sediment transport rate, Ggr

![image.png](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackersimage032.gif) if A < Fgr (6)

![image.png](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackersimage034.gif) if A ≥ Fgr (7)

![image.png](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackersimage036.gif) (8)

The suggested applicability of this equation is for D≥1 and for flows with Froude numbers less that 0.8.

The equations for n, A, M and c have recently been revised and both the original and revised equations are available in the model (sediment transport equations 2 and 3 respectively). The revised equations are:

| For 1 ≤ Dgr ≤ 60, | ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackersimage038.gif) |
| --- | --- |
|  | ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/Ackersimage040.gif) |
| For Dgr > 60, | M = 1.78 |
|  | c = 0.025 |