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# Hydraulic Radius Calculator

To use the Hydraulic Radius calculator, enter the given data, and hit calculate button

## Hydraulic radius calculator

The hydraulic radius calculator evaluates the ratio of the cross-sectional area of a flow channel to its wetted perimeter. It gives the calculation of Hydraulic radius, wetted perimeter, and cross-sectional area.

## What is the hydraulic radius?

Hydraulic radius refers to the ratio of the cross-sectional area of a flow channel to its wetted perimeter. This value is an indicator of the efficiency of flow within the channel.

Engineers and hydrologists use hydraulic radius to analyze the hydraulic performance of rivers, streams, canals, and even pipes.

## The formula of hydraulic radius:

The hydraulic radius is represented by R and its formula is as follows:

R = A / P_{w}

Where:

- R = Hydraulic Radius
- A = Cross-sectional area of the flow
- P
_{w}= Wetted perimeter of the flow channel

## Importance of hydraulic radius in fluid mechanics:

Hydraulic radius plays a vital role in various fluid mechanics calculations such as:

- Determining the flow velocity.
- Shear stress.

Its significance lies in the fact that it characterizes flow efficiency and helps in understanding how efficiently a fluid can move through a given channel.

## Differences between the hydraulic radius and hydraulic diameter:

It is important to distinguish between hydraulic radius and hydraulic diameter. Hydraulic radius applies to open channels and closed conduits with non-circular cross-sections and hydraulic diameter specifically deals with circular conduits. Both parameters serve a similar purpose in different flow scenarios.

## Solved Example:

Consider a rectangular channel having a width of 4 meters and it is 2 meters deep. Find out the hydraulic radius.

**Solution: **

**Step 1:** Extract the data.

Width = 4 meters

Depth = 2 meters

Hydraulic Radius = R =?

The cross-sectional area of the flow = A =?

The wetted perimeter of the flow channel = P_{w} =?

**Step 2:** Find the area and perimeter.

Area = width * depth

Area = 4 * 2

Area = 8

Perimeter = 2 (width + depth)

Perimeter = 2 (4 + 2)

Perimeter = 2 (6)

Perimeter = 12

**Step 3:** Calculations

For hydraulic radius

R = A / W_{p}

R = 8 / 12

R = 2 / 3

**R = 0.67 meters**