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Experiment No 1 To establish the steady uniform flow condition in a laboratory flume and to determine the values of chazy’s constant “C” and manning roughness co-efficient “n” Objective : To establish the steady uniform flow condition in a lab flume . To determine the values of chazy’s constant “c” and manning roughness co-efficient “n”. Apparatus : S6 tilting or lab flume with manometer slope adjusting scale and flow arrangement . Hook / point gauge Related theory : Flume It is a channel which is supported above the ground level and used for experimental purposes. Pipe flow It is a simply the type of plow in which the flow takes under pressure and all the internal parameter wetted. Open channel flow It is the type o flow in which the flow takes under the action of gravity. Flow in the drainage system is the combination of open and pipe flow. Steady flow It is the type of flow in which the flow properties will remains same with respect to time . Uniform flow It is the type of flow in which the flow properties will remains same with respect to distance. In flume steadiness is related to Q and uniformity relates to area of channel. Flow in natural channel is unsteady and non uniform flow. Q varies when we open or close a valve . Assumptions Fluid is an ideal fluid just to simplify the calculations (ideal flow condition) Flow is steady flow Fluid is non viscous Fluid is incompressible hook guage Chazy’s formula It is given by chazy in 1775 V= C V= average velocity C= chazy’s constant depend upon roughness of channel R = hydraulic radius = A/P A = cross sectional area P = wetted perimeter S = channel bed slope This formula is preferable for lined channels. Manning’s formula ; It is given by Robert manning in 1890. V = R2/3 x S1/2 where, n = manning’s roughness co-efficient and depend upon roughness of channel bed S = channel bed slope This formula is generally preferable for unlined channels. RELATION BETWEEN “C” AND “N” Robert manning performed some experiments on chazy’s C and find the C equals to C= R1/6 Like , we know V= C ; V = R2/3 x S1/2 V = R1/6 x R1/2 x S1/2 V = R1/6 x From chazy’s equation V= C so C = R1/6 PROCEDURE : 1. Measure the channel width “B” 2. Adjust some suitable value of slope “S” 3. For the constant value of slope vary the discharge and find the depth of flow of water ( measure at least from three locations ) 4. Find out the values of “C” and “n” OBSERVATION AND CALCULATIONS Channel width “B” = 300 mm = 0.3m slope “S”= 1:400(m/m) h Area Wetted V Depth of flow R =A/P Sr. Discharge (mm) m2 P =Q/A C=V/(RS)0.5 n=(R2/3xS1/2)/V # Q m3/sec (B+2H) h1 h2 h3 mean BxH m m/sec m 1 0.006926 39.2 48.4 46.2 39.60 0.0119 0.3792 0.0313 0.5830 65.8752 0.00852 2 0.008942 55.9 54.7 45.5 47.03 0.0141 0.3941 0.0358 0.6337 66.9821 0.00857 3 0.010195 53.5 60 48.4 48.97 0.0147 0.3979 0.0369 0.6940 72.2420 0.00799 4 0.012326 58 68.5 56.3 55.93 0.0168 0.4119 0.0407 0.7346 72.7851 0.00806 5 0.014693 64.6 74.3 67.3 63.73 0.0191 0.4275 0.0447 0.7685 72.6708 0.00820 6 0.015744 68 76.8 74.8 68.20 0.0205 0.4364 0.0469 0.7695 71.0770 0.00845 7 0.017884 82.3 84 82.5 77.93 0.0234 0.4559 0.0513 0.7649 67.5533 0.00902 8 0.018969 88.3 89.2 82.9 81.80 0.0245 0.4636 0.0529 0.7730 67.1946 0.00912 PRECAUTIONS :- While taking the values of depth of flow the tip of hook gauge should just touch the water surface. Take the piezometer readings when the flow become steady. GRAPH B/W DISCHARGE AND C 74 73 Comments : 72 71 chazy's "c" 70 In graphs points are not as the 69 typical graphs we have but by 68 dropping some points ewe can get 67 the curve similar to typical curve. 66 Q ~ c Calculations shows the variation 65 0 0.005 0.01 0.015 0.02 of “n” and “c” not according to Q (m3/sec) curves. The difference is due to the fluctuation in the depth of flow while performing the experiments GRAPH B/W DISCHARGE AND n that occurs due to small un 0.0087 evenness in the walls of flume. 0.0086 0.0085 0.0084 mannings n 0.0083 0.0082 0.0081 0.0080 Q ~ n 0.0079 Q (m3/sec) Experiment NO 2 To investigate the relationship between specific energy (E) and depth of flow (Y) in a rectangular channel OBJECTIVES:- To study the variation in specific energy as a function of depth of flow for a given discharge in a laboratory flume . To validate the theories of E~Y diagram. APPARATUS : S6 tilting or lab flume with manometer slope adjusting scale and flow arrangement . Hook / point gauge RELATED THEORY : FLUME It is a channel which is supported above the ground level and used for experimental purposes. SPECIFIC ENERGY : it is the total energy per unit weight measure relative to channel bed. E=Y+ ASSUMPTION Normal flow condition exists in channel ( steady flowcondition) Bed slope is very small S<1:10 Velocity correction factor is α= 1.0 DERIVATION: E=Z+ + So = Sf = Sw E = energy per unit weight Α 1 indicates variation in velocities between two sections ENERGY EQUATION AT SURFACE AT TOP = E = ( Z+Y ) + ; = Z+Y+ =C BOTTOM = Z +H+ ; =Z +H+ = C (C = Constant Of Specific Energy ) IN BETWEEN ST Y1 E = (Z+Y1) + (Y-Y1) + (If Channel Bed Is Datum The Z = 0) E=Y+ ; Q = AV ; V = Q/A SO , E = Y + E=Y+ =Y+ =Y+ ( q = (Q/b) (discharge unit width ) >>>>>> E = Y + SPECIFIC ENERGY CURVE (E~Y) DIAGRAM It is the curve which shows the variation in specific energy as the function of depth of flow .Two values of depth at one specific E is called alternate depth one is below the Yc and one is greater than Yc B= min point of specific energy Vc = critical velocity Yc = critical depth corresponding to point B A = same specific energy as C but depth is change Yc = ( )^ DERIVATION : =0 ( Y+ ) =0 1+ x =0 Y^3 = Yc = ( )^ slope adjustment AB curve is known as super critical zone BC curve is known as sub critical zone Region in AB depth is low but velocity is greater that’s why super critical flow Critical depth Yc It is the depth of flow in the channel at which specific energy is minimum FROUD NUMBER: It is the ratio of inertial forces to the gravitational forces . Fr = CRITICAL FLOW It is the flow corresponding to critical depth or it is the flow for which froud No. is 1.0 SUB-CRITICAL FLOW It is the flow with larger depth than Yc and low flow velocity or it is the flow for which froud No. is < 1.0 SUPER CRITICAL FLOW It is the flow with lesser depth than Yc and large flow velocity or it is the flow for which froud No. is >1.0 CRITICAL VELOCITY It is the velocity of flow at critical depth. ALTERNATE DEPTH For any value of specific energy at constant discharge other than critical point. There are two depths one is > critical depth and other is < critical depth these two depths for a given specific energy are termed as alternate depth. EMIN it is the specific energy at critical depth under critical velocity condition in a channel. Relation between Emin & Yc E=Y+ Emin = Yc + = yc + Emin = Yc for only rectangular channel PROCEDURE : 1. Maintain the constant discharge in an open channel . 2. For one particular value of flow find out the water depth at least at three different location and calculate the average depth of flow of water 3. Calculate specific energy using E= Y 4. Repeat this procedure for different values of slope . 5. Draw specific energy curve . 6. Find out critical depth and minimum specific energy . 7. Find Yc theoretical and Ec theoretical Yc th = ( )^ ; Ec th = Yc th = 65.48 mm = 98.22 mm OBSERVATION AND CALCULATIONS: Q = 0.015744 m3/sec ; q = 0.05248 m2/sec ; B = 0.3 m Yc (exp) = 71 mm ; Ec( exp) = 98 mm slope depth of flow (m) E=Y+(q^2)/(2gY^2) sr. no. m/m Y1 Y2 Y3 Y mean (m) 1 0 66.1 83.2 92.3 80.53 0.1022 2 1:500 71 79.9 76 75.63 0.1002 3 1:300 67.6 64 72 67.86 0.0983 4 1:100 42.3 44.6 49.1 45.33 0.1136 5 1:50 31.6 34 39 34.87 0.1503 6 1:40 29.6 31 36.9 32.5 0.1654 GRAPH b/w depth of flow and energy 120 100 80 Y (mm) 60 40 20 E ~ Y ( E =Y) E ~ Y 0 0 20 40 60 80 100 120 140 160 180 E (mm) comparison Yc Ec exp 71 98 COMMENTS : theo 65.48 98.22 The Ec vales are equals but in Yc values some difference that is due to We were using point gauge not hook gauge Practically there was some fluctuations of water depths in the flume Graph of Y ~ E shows that by decreasing the depth of flow head losses increases Observations and calculations shows that by increasing the slope floe changes from sub critical to super critical and Energy of water increases . experiment no 3 To Study The Flow Characteristics Over A Hump Or Weir . Objectives: To study the variation in flow due to introduction of different types of humps and weirs in the flume . apparatus S6 – tilting or lab flume with manometer ; flow arrangement and slope adjusting scale Hook gauge Broad crested weir o Round corner weir o Sharp corner Related theory Weir / hump It is the structure or distribution that is constructed across a river or stream to raise the level of water on upstream side . So that it can be diverted to channel to meet the irrigation requirements . Barrage It is a weir provided with vertical control gate . Types of flow CRITICAL FLOW It is the flow corresponding to critical depth or it is the flow for which fraud No. is 1.0 SUB-CRITICAL FLOW It is the flow with larger depth than Yc and low flow velocity or it is the flow for which fraud No. is < 1.0 SUPER CRITICAL FLOW It is the flow with lesser depth than Yc and large flow velocity or it is the flow for which fraud No. is >1.0 CRITICAL VELOCITY It is the velocity of flow at critical depth. Effect of hump on depth of flow and specific energy. When a hump is provided in a channel bed then specific energy over the hump will reduce in result the depth of flow over the hump will reduced. Consider a simple channel E1 = y1 + ( v12 /2g) E2 = y2 + ( v22 /2g) E3. = y3 + ( v32 /2g) Q and S are constant . and flow is subcritical. Depression appears due to decrease in specific energy over hump. But total energy remain same w.r.t . Channel bed. Up to critical depth if we increase the hump height water will depress but further increase in hump height will not decrease the flow depth over the hump. Critical hump height It is the minimum height of hump which causes the critical depth and critical flow condition over the hump. In super critical flow condition y < Yc and so water level will increase up to yc and then remain constant. Effect of hump height over flow condition If the flow upstream of the hump is sub critical then depth of flow decreases with increase in hump height over the hump up to critical value . Case 1 Hump height is << critical hump height ; Z << Zc Case 2 Z < Zc Case 3 Z = Zc Case 4 Z > Zc Damming action: The height is more than the critical hump height water is sudden increases and hudrulic jump will start. Procedure 1. Fix one particular value of flow (discharge ). 2. For one value of discharge maintain steady flow condition in flume . 3. Install round corner weir in the flume . 4. Measure the depth of flow at various locations. 5. Measure the horizontal distance at each section. 6. Repeat the same procedure for various values of flow. 7. Repeat the same procedure for sharp corner weir. 8. Plot the water surface profiles. Observation and calculation: Channel width = B = 300mm = 0.3m Channel slope = S = 1:400 Table 1: hz distance m weir type width=b ( m ) height =Z ( m ) U/S at hump D/S round 0.4 0.12 4.1 5.3 5.7 sharp 0.4 0.06 4.1 5.3 5.7 Table 2: Flow Q q=Q/b yc Zc Depth of flow mm Weir conditions Sr.# type (m3/s) (m2/s) (mm) (mm) u/s at hump d/s u/s at hump d/s 1 0.0085 0.028277 43.49 114.83 178.8 34 14 sub *sup sup 2 ROUND 0.0120 0.03999 54.79 115.26 195.3 45.4 19.7 sub *sup sup 3 0.0150 0.049877 63.47 116.02 208.3 56.4 26.7 sub *sup sup 1 0.0089 0.029807 45.05 60.33 125 33.4 18.7 sub *sup sup 2 SHARP 0.0117 0.038863 53.75 60.28 136.8 39.7 24.9 sub *sup sup 3 0.0144 0.048063 61.92 60.77 148.3 46 39.3 sub *sup sup *flow over the hump cannot be super critical but in experiment it was . It may be due to the error in discharge gauge ….. Precautions 1. No side space must be there in the flume allowing water to pass by side . 2. The depth measuring needle must be adjusted precisely zero at bottom. 3. The tip of the needle must be just touching the water surface while taking observation. EXPERIMENT # 4 “ To study the flow characteristics of the hydraulic jump developed in lab flume ” Objective To physically achieve the hydraulic jump in lab flume. To measure the physical dimensions of hydraulic jump. To calculate the energy losses through hydraulic jump. To plot the water surface profile of the hydraulic jump for various discharges. Apparatus 1) S6 tilting or lab flume with manometer flow arrangement and slope adjusting scale. 2) Hook gauge RELATED THEORY 1. HYDRAULIC JUMP The rise of water level which takes place due to transformation of super critical flow to the sub critical flow is termed as hydraulic jump. d1 = depth of flow at sec. 1 d2 = depth of flow at sec. 2 d 1 < Yc Super – critical flow d2 < Yc Sub– critical flow why this transformation is occur ? This transformation is occur because flow at super critical condition is unstable and flow tries to stabilize itself that’s why this transformation is take place. 2. Expression for the depth of hydraulic Jump Depth = d2-d1 If d1 is known d1 and d2 give dimensions of hydraulic jump. d2 = - + 3. Expression for loss of energy due to hydraulic jump hL = E1 – E2 by simplifying HL = 4. Length OF HYDRAULIC Jump Distance between two sections where one section is taken just before the hydraulic jump and second section is taken just after the hydraulic jump is termed as the length of hydraulic jump. Length = 5-7 times of depth 5. LOCATION OF HYDRAULIC JUMP Location of jump depends upon d2 and Y2 Y2 = Normal depth of flow on downstream side. Strength of hydraulic jump is the amount of energy dissipation Case No. 1 d2 < y2 Jump is forming over the glacis and it is a weak jump. Case No. 2 d2 = y2 Energy dissipated in this jump is more than in Case No. 1 . Jump is forming at toe. Case No. 3 d2 > y2 Hydraulic jump is away from structure . Depth of floor is less so it will damage the floor. So Ideal Case will be Case No. 2 as structure is safe and relatively stronger energy dissipation. If Case No. 2 does not fit accordingly to the conditions then Case No 1 will be use as it has less energy dissipation but it is safe but Case No. 3 will never be adopted as it is unsafe TYPES OF HYDRAULIC JUMP Controlling section is section 1. Fraud No at Section (1) F1 I. F1 < 1 Sub - Critical flow II. F1 = 1 Critical flow (No hydraulic jump) III. F1 = 1 – 1.7 Undular hydraulic Jump IV. F1 = 1.7 – 2.5 Weak Jump V. F1 = 2.5 – 4.5 Oscillating Jump VI. F1 = 4.5 – 9.0 Steady Jump VII. F1 > 9.0 Strong Jump PRACTICAL APPLICATIONS OF HYDRAULIC JUMP To dissipate the energy of water flowing over the hydraulic structure and thus prevent scouring on the downstream side. To recover the head or raise the water level on downstream side of the hydraulic structure and thus to maintain high water level in the channel for irrigation or other water distribution purposes. To mix the chemicals for different water treatment presses. To increase the weight on apron and thus reduce the uplift pressure under the structure by raising the water depth on Apron. Apron: A layer of flexible material PROCEDURE Fix one particular value of slope. Change the discharge for every reading. Measure the depth of flow at describes locations/ sections. Measure the horizontal distance at each section. Repeat the same procedure for five discharges. Plot the data in one Graphs. The hydraulic jump produced in the flume Due to back water effect. Observations and calculations DEPTH LENGTH HORIZONTAL DISCHARGE DEPTH OF FLOW OF OF V1= DISTANCE YC JUMP JUMP HL F1= SR. TYPE OF NO JUMP Q Y Y1 Y2 X X1 X2 Y2 - Y1 X2 - X1 V1/ m3/sec m m m m m m m m m m m/sec 1 0.011659 0.0253 0.0233 0.0904 7 7.2 7.38 0.054 0.0671 0.18 0.0359 1.668 3.488765 2 0.0144 0.0295 0.028 0.1 7 7.45 7.65 0.062 0.072 0.2 0.0333 1.714 3.270918 OSCILLATING JUMP 3 0.015744 0.0305 0.031 0.102 7 7.54 7.71 0.066 0.071 0.17 0.0283 1.693 3.069847 F in the range of 2.5- 4 0.017659 0.0325 0.0354 0.109 7 7.65 8.05 0.071 0.0736 0.4 0.0258 1.663 2.821665 4.5 5 0.019792 0.0374 0.038 0.117 7 7.76 8.06 0.076 0.079 0.3 0.0277 1.736 2.843535