CE 3620: Water Resources Engineering Spring 2015 Lab 7: Nonuniform Flow and Open Channel Transitions BACKGROUND An open channel transition may be defined as a change either in the direction, slope, or cross section of the channel, which produces a change in flow conditions, and thereby results in nonuniform flow. Most transitions of engineering interest are comparatively short structures, although they may affect the flow for a great distance upstream or downstream. Transition sections are needed where conduit or channel cross sections, and consequently velocities, are appreciably changed. Their purposes are to prevent disturbances in flow, minimize losses of head where velocities are increased, and recover as much velocity head as possible where velocities are decreased. An open channel expansion may be defined as an increase in cross-sectional flow area of the channel in the direction of flow, thereby decreasing the mean velocity of the flow. The flow conditions in the outlet channel are complicated by the likelihood of flow separation along one expansion wall, or both, if the rate of change of cross-sectional flow area is too rapid. Usually, the engineer is interested in minimizing the length of the structure in order to minimize construction costs, which requires a rapid increase of cross-sectional flow area. Thus, a balance must be sought between economics and the importance of minimizing energy losses, as well as an accounting of downstream erosion if an earthen outlet channel is to be used. In this lab, you will build on concepts discussed in lecture and in Lab 5 to further investigate the effects of contractions and expansions on open channel flow. You will use the flume in Dillman 110 with added segments as shown in Figure 1 below. Figure 1: Schematic of the channel with contraction and expansion. Three cross sections will be analyzed. 1
LAB OBJECTIVES To develop specific energy diagrams by measuring flow depth (y) and flow rate (Q). To develop water surface profiles (WSP) plots. To compare the percent difference in specific energy between three cross sections in the channel. Calculate headloss from a contraction and expansion EXPERIMENTAL PROCEDURE 1. Your TA will set the flow rate to the lowest flow (0.07 cfs). Observe how the flow depth changes throughout the contraction and expansion. 2. The first task is to create a WSP of the water depth in the channel using the point gauge to measure the depth. Notice that values on the gauge go from small (top) to large (bottom). Start at cross section ZERO (marked on the side of the channel as CE3620 ZERO ). Drop the point gauge to the bottom of the channel, and record the measurement in Table 1 of the attached data sheet. This is our base reading. Similar to the weir experiment, we will subtract this value from all WSP readings to obtain the flow depth (y). The channel is assumed to be horizontal (slope of zero). 3. At the same section, move the point gauge up until the tip is barely touching the surface of the water. Take reading, and have someone with a calculator subtract the base value from your reading. Record this difference in Table 1 as the flow depth (y) in mm. 4. Move the point gauge downstream and continue to take water surface readings. Make sure to take enough readings in order to create an accurate WSP throughout the contraction/expansion and to cross-section 3 (see Figure 1), and record both distance (x) moved from cross section ZERO and flow depth (y). 5. Record the flow depth at the three cross sections (see Figure 1) in Table 2. The x- direction locations have been marked for you. 6. Repeat all steps for two more flow rates. RESULTS For each flow rate, compare values of the specific energy obtained experimentally across the three sections indicated in Figure 1. In addition, use your computed specific energy values to evaluate headloss across the contraction and expansion for each flow rate. Record measurements taken during lab in the tables on the attached data sheet. Type these results up in a spreadsheet and include them in the report 2
CALCULATIONS Show sample calculations for one trial (i.e., for one flow rate) as outlined below. Label variables and use units in your calculations. Make sure to show all equations used, as well as any unit conversions. Using flow depth measurements in Table 3 and the corresponding flow rate, calculate the specific energy (E) at cross sections 1, 2 and 3. Record these values in Table 4. = + Neglecting headloss, compute the % difference between E 1 & E 2, and E 2 & E 3. See the energy equation written for cross-section 1 to 2 below, which reduced to E 1 = E 2 when headloss is neglected in a horizontal channel. Record these values in Table 5. + = + (without headloss) Calculate headloss (h L ) from cross-section 1 to 2, and from 2 to 3. Record these values in Table 7, and the corresponding values of the friction slope (S f ) in Table 6. Values of contraction/expansion coefficients (K M ) are provided in Table 3. h ( ) = + = ( /") (n = 0.013 for Wood) Compute the % difference between E 1 & (E 2 + h L(1-2) ) and E 2 & (E 3 + h L(2-3) ) in order to account for headloss. See the energy equation below written for cross-section 1 to 2, wherein the headloss term is included on the downstream (right hand) side of the equation. Record these values in Table 8. + = + +h (with headloss) Calculate critical depth for the main channel (y c1 for B = 3 ft) as well as within the contraction (y c2 for B = 2 ft) for all three flows. Also, compute the corresponding minimum specific energy in each case. " # = $ % & (for rectangular channel) GRAPHS 1. Create three WSP plots (one for each flow rate). Indicate the location of the contraction and expansion on graph. Make sure to connect points with a smooth curve. Place two horizontal lines on each graph indicating critical depth for the main channel (y c1 ) as well as within the contraction (y c2 ). This will help show where the flow is crossing through critical depth into supercritical conditions, as well as jumping back up to subcritical conditions. Make sure all axes are properly labeled with correct units. 3
2. Create three specific energy diagrams (one for each flow rate) which include the following information: Two curves denoted q 1 and q 2 where q denotes the flow rate per unit width (Q/B). Locations of critical depths (y c1 and y c2 ) in main channel as well as in contraction. Locations of minimum specific energy on both curves, corresponding to y c1 and y c2. Locations of cross sections 1, 2 and 3 on curves q 1 and q 2. Be careful placing points either above or below critical depth (subcritical or supercritical). Recognize which type of flow is in operation. Recall that for subcritical conditions y > y c, and for supercritical flow y < y c. DISCUSSION 1. How do the differences in specific energy neglecting headloss (Table 5) compare to the differences reported in Table 8? Is all of the headloss observed accounted for by effects of friction (based on S f ) and the contraction/expansion? 2. The TA will remove the gradual contraction and expansion blocks. What do you observe? What type of flow patterns are seen? What issues could occur if this situation took place around an abrupt bridge abutment? See Figure 2. 3. Consider the trial with the highest flow rate. In this case, we saw the channel was not long enough for the water to jump back up to subcritical flow. Why could this create issues in natural streams /rivers? What are some ways that civil/hydraulic engineers deal with this issue (i.e. what can be designed in order to control the location of the hydraulic jump)? Figure 2: Flow patterns around a bridge abutment. www.fhwa.dot.gov 4
DATA SHEET Table 1. Water Surface Profile Measurements Bottom of Channel ( Base ) Reading: mm x - Distance (cm) Flow Depth, y (mm) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 5
Table 2. Flow depth measurements for cross sections 1 3. x - Distance (cm) Flow Depth, y (cm) 1 0 2 85 3 250 Table 3. K M values for headloss equation. K m Values Type Contraction Expansion Gradual 0.15 0.3 Bridge 0.3 0.5 Abrupt 0.6 0.8 Table 4. Specific energy (E) for cross sections 1 3. x - Distance (cm) Specific Energy, E (cm) 1 0 2 85 3 250 6
Table 5. Percent difference comparing specific energy (E) from cross sections 1 2 and 2 3. Ignoring Headloss % Difference without h L 1-2 2-3 Table 6. Coefficient S f Friction Slope (S f ) 1 2 3 Table 7. Headloss values from cross sections 1 2 and 2 3 for all flow rates. Headloss (h L ) cm 1-2 2-3 7
Table 8. Percent difference comparing energy equation from cross sections 1 2 and 2 3. Including Headloss % Difference with h L 1-2 2-3 8