FLUME AREA CALCULATION

Transcription

1 FLUME AREA CALCULATION 1. Introduction The models used at Pelaez Ranch are trapezoidal shape flumes. The sizes of flumes are different due to the volume of water passing from them. This SOP explains how to measure the amount of water, area (volume of water) inside the flumes in a specific time. Flume model - 3 feet 60 V is used in stations 1, 2, 3 and 4. Model 2 ft SRCRC is used in station 5. Here is the description table of both models: Station Description B1 B2 a B W D H1 1, 2, 3, 4 3 feet60º V / ½ 5 2 ft SRCRC Table 1. Dimensions of the flumes The first model-3 feet 60 V can operate up to gpm (gallons per minute), and the second-2 ft SRCRC, can operate from 21 to gpm. The dimensions in table 1 refers to the sketches below: Figure 1. Plan view related to table 1.

2 Figure 2. End and Section view related to table 1. Measuring the water depth (upstream is taken as a base) in inches with a ruler at the field, we can calculate the area using the equations studied in this SOP. So we can find the flow as Q = V (velocity ) x A (area) All the data and the consequent conclusions are from 25-July-05. On that day only station 4 velocity was measured and taken as a pattern. Flow, Q can be calculated just with velocity >0. More information can be reached from

3 Here is a resume of the information needed to do the calculations of the flume areas. Figure 3. Measurements of the area equation. The depth is measured upstream from the throat a distance of 3 to 4 times the maximum expected head. This location is somewhat arbitrary because the head does not vary too much with position. It is important to note that head is measured from the top of the hump rather than from the bottom of the approach channel. Regarding analysis of flumes, flumes (like weirs) are designed to force a transition from sub-critical to super-critical flow. In the case of flumes, the transition is caused by designing flumes to have a narrowing at the throat, raising of the channel bottom, or both. Such a transition causes flow to pass through critical depth at the flume throat. At the critical depth, energy is minimized and there is a direct relationship between water depth and velocity (and flowrate). However, it is physically very difficult to measure critical depth in a flume because its exact location is difficult to determine and may vary with flowrate. Through mass conservation, the upstream depth is related to the critical depth. Therefore, flowrate can be determined by measuring the upstream depth, which is a highly reliable measurement.

4 2. Equations and Methodology Till now, we have been using just the area equations, but others may be useful for the future equations based on ISO 4359, 1983: [2] Let H=h and obtain C s from the graph below. Note that the graph is only valid for 0.02 < mh/b < 5. Then, C v from numerical solution of:

5 C v can only be computed if hbc s /A<0.93. Since C s and C v are functions of both H and h, re-compute H=h C v 2/3, C s, C v, and Q. ISO 4359 suggests re-computing Q three times, but we re-compute Q until there are at least four significant digits of accuracy. Then, V and F are computed from the final Q. 3. Variables m- meters, s- seconds A- Cross-sectional area of approach channel [m 2 ]. B - Bottom width of flume throat [m]. B - Bottom width of approach channel [m]. C - C d - Coefficient of discharge for rectangular, trapezoidal and U flumes [unit-less]. C s - Shape coefficient for trapezoidal flume [unit-less]. C v - Coefficient of approach velocity for rectangular, trapezoidal, and U flumes [unitless]. F - Froude number of flow in approach channel [unit-less]. F<1 is slow or sub-critical flow. F>1 is fast or super-critical flow. g - Acceleration due to gravity, m/s 2. h - Measured head [m]. If there is a hump, then it is the vertical distance between the top of the hump and the water surface. H - Total head [m]. Measured head plus velocity head. H=h C v 2/3 k - Constant used in trapezoidal flume computation [unit-less]. L - Length of flume throat [m]. m - Side slope of trapezoidal flume throat. Horizontal to vertical (H:V). M - Side slope of trapezoidal flume approach channel. Horizontal to vertical (H:V). P - Hump height [m]. Q - Flowrate through flume [m 3 /s]. T - Top width of approach channel [m]. V - Velocity in approach channel [m/s]. 4. Data analysis Based on the equation of the area, it is done a excel page. Almost all the values are constants based on the flume description from the top.

6 The values that need to be change each time are: Velocity, it should be calculated. Also the P+ H, it is what we measure in the flumes with the ruler. Since my concern P is always equals 0, to understand what is P and all the abbreviations check the introduction. The other values are constant. See below an example of the results given by the excel model. This results are the ones achieved on Station area ( inches 2 ) area (feets 2 ) Velocity (f/s) q (cfs) station (inches) P H B M P + H area