UNIT 4 Unsteady Flow.pptx

Unsteady flow:
Equation of motion for unsteady flow,
Celerity of the gravity wave,
deep and shallow water waves,
open channel positive and negative surge.
The flow of water in rivers, canals, reservoirs, lakes, pools, and free- surface flow in storm water drains, conduits, pipes , galleries, tunnels and culverts, in which the velocities change with time, is defined as unsteady flow ( non - permanent, non - stationary , or time -variable free- surface water flow).

This unsteadiness may arise naturally or may be caused by human action. Floods in rivers, water level variation in estuaries due to tidal action etc. are examples of unsteady flows occurring naturally.

Surges created in power channels, water level variation in irrigation canals due to gate operation etc. are unsteady flows caused by human action

1. Unsteady Flow Unsteady flow: Equation of motion for unsteady flow, Celerity of the gravity wave, deep and shallow water waves, open channel positive and negative surge.

2. The flow of water in rivers, canals, reservoirs, lakes, pools, and free- surface flow in storm water drains, conduits, pipes , galleries, tunnels and culverts, in which the velocities change with time , is defined as unsteady flow ( non - permanent, non - stationary , or time -variable free- surface water flow). This unsteadiness may arise naturally or may be caused by human action. Floods in rivers, water level variation in estuaries due to tidal action etc. are examples of unsteady flows occurring naturally. Surges created in power channels, water level variation in irrigation canals due to gate operation etc. are unsteady flows caused by human action. Analysis and computation of unsteady flow in open channels are important from the point of view of operation of flood control reservoirs, designing a flood forecasting system, risk assessment of dam breaks, designing storm water drainage systems, and assessment of surface irrigation systems. Unsteady Flow

3. Gradually varied unsteady flow occurs when the flow variables such as the flow depth and velocity do not change rapidly in time and space. Such flows are very common in rivers during floods and in canals during the period of slow variation in gate opening or closure. Typically two flow variables, such as the flow depth and velocity or the discharge and depth, define the flow conditions at a channel section. Two governing equations, known as Saint Venant equations, are used to descrine the spatial and temporal variation of the above two flow variables. These equations are based on the application of conservation of mass and momentum principles to a stationary control volume. GRADUALLY VARIED UNSTEADY FLOW

4. In Figure below, if Q2 > Q1, more flow goes out than what is coming into Section 1. The excess volume of outflow in a time Δt is made good by the depletion of storage within the reach bounded by Sections 1 and 2. As a result of this the water surface will start falling. If Δt = distance between Sections 1 and 2, Equation of Continuity For Unsteady Flow

5. The above equation is the basic equation of Continuity For Unsteady Flow.

6. SURGE AND CELERITY IN UNSTEADY FLOW

7. The sudden changes of flow in open channel results in the increase or decrease of flow depth is called the "SURGE" in open channel. This could take place when there is a breaching of dams due to earthquake or regulating the hydropower sluice gates. Hence results in positive and negative surges in downstream river channel or in downstream tail channel of hydropower projects. This phenomenon also governs when there would be flood (unsteady flow) during monsoon period in natural river channels and the hydrograph significantly varies with rising and falling as the rainfall takes it peak period. The flood wave which generates during the positive or negative surges is called the wave velocity of the flood in unsteady flow situation. This positive or negative surge sometimes travels downstream or upstream depending on the situation. The increase in flow depth would become the crest of the surges and the decrease in the flow depth would become the trough of the surges. SURGE

8. A stationary observer therefore sees an increase in depth as the wave front of a positive surge wave passes. A negative surge wave, on the other hand, leaves a shallower depth as the wave front passes.

9. Find the sequent depth and energy loss in a hydraulic jump in a rectangular channel 4.3m wide 0.5m deep. The discharge through channel is 8.9cumec. [4.15m, 0.68m] E l = (y2-y2) 3 / 4y1y2 2. A hydraulic jump occurs in horizontal rectangular channel with sequent depths of 0.25m and 4.9 m. Calculate the rate of flow per unit width, energy loss and initial Froude number. 3. The depth of flow of water, at a certain section of a rectangular channel of 6m wide, is 1m. The discharge through the channel is 24 cumecs . If a hydraulic jump takes place as the d/s side, find the depth of flow after the jump. 4. Surge travels upstream at a velocity of 3m/s. If the steady state velocity in the channel was, 0.6m/s and flow depth in channel is 1m. Calculate the celerity and height of the surge. NUMERICAL PRACTICE

10. 4. Surge travels upstream at a velocity of 3m/s. If the steady state velocity in the channel was, 0.6m/s and flow depth in channel is 1m. Calculate the celerity and height of the surge. Surge – downstream C = Vw-V1 upstream C = Vw +V1 height = y2 – y1 C = (.5 g (y2/y1) (y2+y1)) 1/2 If y2 is small appx = y1 C = ( gy ) 1/2 Y1 (Vw-V1) = y2(Vw-V2)

11. The upstream positive surge wave The front of the surge wave is propagated upstream at celerity, c, relative to the stationary observer. To the observer, the flow situation is unsteady as a wave front passes; to an observer travelling at a speed, c, with the wave the flow appears steady although non-uniform. The following fig shows the surge reduced to steady state.