Hydraulic Jump

UET Hydraulic Engineering Lab

Experiment No. 4 To study the flow characteristic of a Hydraulic Jump developed in lab flume. Objective 1) 2) 3) 4)

To physically achieved the hydraulic jump in lab flume. To measure the physically the dimension of hydraulic jump. To calculate the energy losses through hydraulic jump. To plot the water surface profile for hydraulic jump at various discharge.

Apparatus I. II.

S6 – Tilting / lab flume with manometer, slope adjusting scale and flow arrangement Hook gauge

Related Theory: Hydraulic Jump The raise of water level which takes place due to transformation of supercritical flow to the sub critical flow is termed as hydraulic jump. Proof: E.L

hL

d2 Sec .1

Sec. 2

d1

(fig.1) M.Safdar, 2007 – CIVIL - 48

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UET Hydraulic Engineering Lab

hL

E.L y

d1 E = y + V2/2g

fm = q2/yg + y2/2

d2

(fig.2) For channels on gradual slope (i-e less than about 3°) gravity component of weight is relatively small and may be neglected without introducing significant error. The frictional forces acting are negligible because of short length of channel involved and therefore only significant forces are hydrostatic forces. Applying Newton’s 2nd law to the element of fluid contained b/w section 1 and 2 as shown in fig.1. ∑Fx = Rate of change of momentum ∑Fx = γhc1A1 - γhc2A2 =

(V2 – V1)

Which can be reordered too give Q V1 +γhc1A1 = Q V2 +γhc2A2 ………………..1 This states that the momentum plus the pressure force on cross sectional area is constant, or dividing by γ and observing that V = Fm =

M.Safdar, 2007 – CIVIL - 48

+ Ahc = constant ………………….2

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UET Hydraulic Engineering Lab

This equation applies to any shape. In case of rectangular channel, this reduces for unit width (B = 1) to: q= =

, A = By = 1.d = d, hc = d

fm =

=

……………3

A curve of values of fm for different values of y is plotted to the right of specific energy diagram as shown in fig. 2. Both curves are plotted for the condition of q m³/sec per m of width. As the loss of energy, in jump does not affect the “force” quantity fm , the latter is the same after the jump as before. Therefore any vertical line intersecting the fm curves to locate two conjugate depth d1 and d2. These depths represent possible combination of depth that could occur before and after the jump. When rate of flow and depth before are after the jump is given as seen in equation 3 becomes a cubic equation when solving for the other depth. This may readily reduced to a quadric equation however by observation that d22 - d21 = (d2 – d1) (d2 + d1) From equation 3

= = –

= = d1d22 + d21 d2 -

= 0 ………………..4

d2d21 + d22 d1 -

= 0 ………………..5

By solving these two quadric equations we get M.Safdar, 2007 – CIVIL - 48

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UET Hydraulic Engineering Lab

d2 =

…………… A

Or q = v1d1 = v2d2 d2 =

………………..

d1 =

…………… B

Or q = v1d1 = v2d2 d1 =

………………..

Depth of Hydraulic Jump: D = d 2 – d1 D=

Expression for loss of energy due to Hydraulic Jump: hL = E1 – E2 hL = hL = d1 – d2 + For q = v1d1 = v2d2

hL = d1 – d2 + hL = d1 – d2 + Put

=

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UET Hydraulic Engineering Lab

hL = d1 – d2 + By simplifying we get hL = hL =

…………………(C)

Length of Hydraulic Jump: It is the length between two section where one section is taken before the hydraulic jump and 2nd section taken after the hydraulic jump is termed as the length of hydraulic jump. For rectangular channel = length of hydraulic jump = 5-----7 times the depth of hydraulic jump.

Location of Hydraulic Jump: There are two factors which decide the location of hydraulic jump. Y2 = normal depth of flow on the down stream side of hydraulic jump d2 = depth of flow just after the hydraulic jump

Case # 1

d2 < Y 2

In this case hydraulic jump is weaker. (Less energy deception)

Y2

d2 M.Safdar, 2007 – CIVIL - 48

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UET Hydraulic Engineering Lab

Case # 2

d2 = Y 2

This case is formed at the toe. It is preferable case. If this case not formed then we have case #1.

Y2

d2

Case # 3

d2 > Y 2

This case is not preferable. In this case energy deception is more. If more energy is dissipated it means that strength of hydraulic jump is more. More d2 more energy is dissipated.

Y2

d2

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UET Hydraulic Engineering Lab

Types of Hydraulic Jump: Froude No. (Fr)

Type of H.J

1 1-1.7 1.7-2.5 2.5-4.5 4.5-9 >9.0

No Jump Undular Jump Weak Jump Oscillating Jump Steady Jump Strong Jump

Practical Application of Jump: 1. To decapitate the energy of water flowing over the hydraulic structure and thus prevent the scouring on D/S floor. 2. To recover the head or raise the water level on the down stream side of hydraulic structure & thus to maintain high water level in the channel for irrigation and other water distribution purposes. 3. To increase the weight on apron thus reducer the uplift pressure under the structure by raising the water depth. 4. To mix chemical for water purification.

Procedure I. II. III. IV. V. VI.

Fix one particular value of slope. For one value of discharge maintain steady flow conditions in the flume. Develop the hydraulic jump. Measure the depths yo,y1,& y2 & corresponding horizontal distance xo,x1 and x2. Repeat the procedure for various discharges. Plot water surface profile.

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UET Hydraulic Engineering Lab

Observation & Calculation Channel width = B = 300mm = 0.3m Channel slope = S = Sr. No

1 2 3 4 5

Q

Depth of flows (mm)

Hz. Distance (m)

yc

depth of jump (m)

length of jump (m)

hL

V1 = Q/By1

m3/s

y0

y1

y2

x0

x1

x2

m

y2-y1

x2-x1

m

m/s

0.012646 0.013863 0.015428 0.016966 0.019178

26.00 30.23 35.00 37.00 36.00

44.0 40.8 49.0 50.0 45.0

98.0 100.5 100.0 113.0 110.0

8.80 8.80 8.80 8.80 9.00

9.26 9.34 9.42 9.51 9.59

9.56 9.56 9.56 9.70 9.83

0.057 0.060 0.065 0.069 0.075

0.054 0.060 0.051 0.063 0.065

0.00030 0.00022 0.00014 0.00019 0.00024

0.0091 0.0130 0.0068 0.0111 0.0139

0.958 1.133 1.050 1.131 1.421

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Fr

Type of Jump

1.46 Undular 1.79 Weak 1.51 Undular 1.61 Undular 2.14 Weak

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UET Hydraulic Engineering Lab

Water Surface Profiles for Hydraulic Jump: 12

Depth (y,cm)

10 8 Q = 0.012646m3/s 6

Q = 0.013863m3/s

4

Q = 0.015428m3/s Q = 0.016966m3/s

2

Q = 0.019178m3/s

0 850

900

950

1000

Horizontal Distance (x,cm)

Precautions i. ii.

During taking the values of depth of flow, the tip of hook gauge should just touch the bottom surface. Take man metric reading when flow is steady.

Comments  There are two type of jump formed in the experiment as shown in table.  Undular jump formed when Fr = 1----1.7 and weak jump is formed when Fr = 1.7-----2.5.  The experiment is simple to draw the hydraulic jump.

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