To study water surface profiles on steep slope

Objectives:

1. To set the steep slope in S6 tilting flume
2. To observe S1 & S3 profiles in flume when sluice gate is provided.
3. To draw water surface profiles when sluice gate is provided in flume.

Apparatus:

1. S6 tilting flume
2. Point gauge
3. Sluice gate

Related theory:

Gradually varied flow:

If the flow depth varies at slow rate with respect to distance then the flow is called gradually varied flow.

Rapidly varied flow:

If the flow depth varies significantly in a short distance then the flow is called rapidly varied flow.

Governing equation for gradually varied flow:

The gradually varied flow equations in a prismatic channel having no lateral inflow or outflow are derived in this section by making the following simplifying assumptions:

1. The slope of the channel bottom is small.
2. The channel is prismatic channel and there is no lateral inflow or outflow from the channel.
3. The pressure distribution is hydrostatic at all channel sections.
4. The head losses in gradually varied flow may be determined by using the equations for head losses in uniform flows.

The governing equations for G.V.F are given below:

Classification of water surface profiles:

Channel-bottom slopes are classified into the following five categories:

Mild, steep, critical, horizontal (zero slope) and adverse (negative slope). The first letter of these names refers to the type, i.e., M for mild, S for steep, C for critical, H for horizontal and A for adverse slope.

The bottom slope of a channel is called as mild slope if the uniform flow is subcritical (i.e., yn > yc); for the specified discharge and Manning n; it is critical slope if the uniform flow is critical (i.e., yn = yc); and it is steep slope if the uniform flow is supercritical (i.e., yn < yc). It is apparent that the normal depth is infinite if the bottom slope is horizontal and it is nonexistent if the bottom slope is negative. To summarize, the channel bottom slope is called

• mild if yn > yc;
• steep if yn < yc; and
• critical if yn = yc.

Note:

If surface profile lies above both lines i.e. y_o and y_c, it is called type 1 profile

If surface profile lies between these lines i.e. y_o and y_c, it is called type 2 profile

If surface profile lies below both lines i.e. y_o and y_c, it is called type 3 profile

Observations:

All type 1 surface water profiles are formed due to dams or weirs.

All type 2 surface water profiles are formed due to brink.

All type 3 surface water profiles are formed due to sluice gate on downstream.

Steep slope:

When slope of channel is steep then,

S_o>S_c

y_n<y_c

Zone 1 (S1 Profile)

Since y>yc>yo in zone 1, the numerator is + and denominator is also +, hence the slope of surface profile in zone 1 is increasing.

Zone 2 (S2 Profile)

Since yc>y>yo in zone 2, the numerator is + and denominator is also -, hence the slope of surface profile in zone 1 is decreasing.

Zone 3 (S3 Profile)

Since yc>yo>y in zone 3, the numerator is – and denominator is also -, hence the slope of surface profile in zone 1 is increasing.

Water surface profiles on different slopes along with practical application

Procedure:

1. Set some suitable value of slope in flume, this slope should be steep slope (this will be confirmed by calculating whether y_n<yc or not)
2. Allow discharge in the flume and note its value.
3. By using manning’s equation find the normal depth in the flume using the fixed discharge value.
4. Also find the critical depth using the fixed discharge value.
5. Check whether yn<yc or not, if this is satisfied then this will be the steep slope and now we can measure the depth of water.
6. Measure the water surface profiles by changing the gate openings of sluice gate but keeping gate opening less than yn.
7. Draw water surface profiles at various gate openings.

Observations and Calculations

Q= 0.014693 m³/s

b= 300 mm

Slope 1:50

Sluice gate is provided at 4.85 m

Finding normal depth:

As yn<yc, hence steep slope confirmation.

Readings of water depths:

Gate opening	<yn	<yn	<yn	≈yn
	20mm	30mm	40mm	45mm
Distances	Depths
x	y	y	y	y
mm	mm	mm	mm	mm
2000	180	121	36	35
2500	205	136	74	34
3000	228	148	89	32
3500	249	160	103	33
4000	268	174	116	80
4500	288	187	130	102
4750	303	193	139	110
4900	15	21	29	30
5000	16	21	27	29
5500	21	28	26	28
6500	23	28	29	31
7500	19	26	25	31
8500	20	27	26	28

Conclusions:

1. The water surface profile S1 & S3 are formed on steep slope when sluice gate is provided at opening of sluice gate < yo
2. Hydraulic jump is formed on upstream side of sluice gate when opening of sluice gate is < yo

 

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