Rapidly Varied Flow and Hydraulic Jump | Types of Liquid Flow and Froude Number

If the flow depth is rapid over a short distance, then flow is Rapidly Varied Flow and if the flow depth is changing gradually over a long distance, the flow is Gradually Varied Flow. Rapidly Varied Flow and Gradually Varied Flow are steady and non-uniform flows.

Rapid and Gradually varied flow

Coming to the definition

Rapidly Varied Flow (RVF) is a significant change in water depth or velocity of flow over a short distance. This distance can be a few times the water depth. Gradually Varied Flow (GVF) is the flow where the water depth changes gradually over a large distance. Hydraulic jump is an example of rapidly varied flow, where the liquid level rises suddenly.

Types of Fluid Flow

Flow takes place in an open channel, the free water surface is at atmospheric pressure. Flow takes place due to gravitational force. Examples are flows in the river, canal, sewage, etc.

Steady flow

In steady flow, the rate of flow (Q), depth of flow (y), cross sectional area of channel (A) and velocity of flow (v) remain constant with time.

Example: Flows in the river, canal

Unsteady flow

The rate of flow (Q), depth of flow (y), cross sectional area of channel (A) and velocity of flow (v) keep changing with time.

Example: Floods, surges, etc.

Uniform flow

In uniform flow Q, y, A, V remain constant over the length of the channel.

Non uniform flow

In non uniform flow Q, y, A, V keep changing over the length of the channel. There ate two main types of non-uniform flow. One is gradually varied and the other one is rapid varied flow.

Gradually Varied Flow (GVF): Flow depth changes gradually. Example: Dam placed in the middle of the flow.

Yep, I understand, you want more on this. So, I already have a video ready for you. Go for it!

Rapidly Varied Flow (RVF): Flow depth changes very rapidly. Example: water released over the spillway.

Rapid flow is an important and frequently asked topic in GATE, IES and various competitive exams. No need of looking here and there, this video will suffice!

Reasons for Varied Flow

Varied flow occurs where there is a local turbulence/disturbance to the balance between gravity and friction (such as at a weir, sluice, free overfill, sudden change in slope) or inconsistency between the depths imposed by downstream and upstream controls (hydraulic jump). The depth variation also changes the velocity of flow over the span.

Hydraulic Jump

When a supercritical stream meets with a subcritical stream of sufficient depth , energy is lost in the form of eddies and the flow depth changes suddenly, which is termed as the hydraulic jump.

It forms when a shallow stream of water with supercritical velocity strikes the water having a large depth of flow and subcritical velocities. For example-

  • downstream of a sluice gate on a mild slope

  • at bottom of spillway

  • steep slope changes to mild slope

Hydraulic jump is used as an energy dissipater to avoid the erosion of the channel. Stilling basin is arranged downstream, when water comes from upstream and hits this stilling basin with required subcritical depth, then the rollers will form and hence the hydraulic jump is formed.

Application of hydraulic jump

Hydraulic jump is used for mixing the chemicals in the water purification. It is also used in the aeration of the sewage water.

Hydraulic jump also helps in increasing the height of the apron to reduce the uplift pressure.

  • Before introducing the apron blocks, there exists high head difference, then the water starts seeping from upstream to downstream, then the uplift pressure at downstream.

  • So to reduce the uplift pressure, we arrange some blocks downstream , then the head difference will reduce due to the hydraulic jump and uplift pressure is reduced.

It is also plays an important role at sluice gate opening.

Types of hydraulic jump

Hydraulic jump is classified depending upon the Froude number of incoming flow.

Undular/regular jump

  • Undular water surface

  • No proper hydraulic jump Relative energy loss <5%

Weak jump

  • Some surface rollers will start to form

  • Relative energy loss 5 to 8%

Oscillating jump

  • Rollers will form

  • Oscillation of water between the bed and water surface

  • Still the energy dissipation is not sufficient

  • Relative energy loss is 18-45%

Steady jump

  • Properly formed rollers

  • Jump formed properly and the surface gets smoothen after the jump

  • The relative energy loss 45-70%

Strong jump

  • Surface is rough, proper jump and rollers are formed

  • Surface remains rough after the jump

  • Relative energy loss is >70%

Froude number (Fr)

Froude number is a dimensionless value that explains various flow regimes of open channel flow. This number is the ratio of inertial and gravitational forces.

The formula of Froude Number(Fr) goes like-

Fr = V / sqrt(gD)

Where, V: Average velocity of the liquid in a channel

g: Acceleration due to gravity

D: Hydraulic depth (=Cross sectional area of flow/top width)

  • Froude number for Regular Jump ranges from 1.0 to 1.7

  • Froude number for Weak Jump ranges from 1.7 to 2.5

  • Froude number for Oscillating Jump ranges from 2.5 to 4.5

  • Froude number for Steady Jump ranges from 4.5 to 9.0

  • Froude number for Strong Jump is more than 9.0

Specific force is a very important section of hydraulic jump. It is the sum of pressure force and momentum force per unit weight and it remains constant between 2 sections. We will see more on this in the upcoming article.

Flow types based on Froude Number

  • Critical flow: Froude Number = 1

  • Subcritical flow: Froude Number < 1

  • Supercritical flow: Froude Number > 1

Match the columns and understand Froude Number better!

Closing it up here! I am planning to make another article on momentum equation, specific force and sequent depths. Let me know by commenting on what all you want for the next one.

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