Fluid mechanics work

1

KNE351 Fluid Mechanics 1

Laboratory Notes

Broad-Crested Weir

This booklet contains instructions and notes for the experiment listed above. Additional material relating to laboratory work will be delivered during the course. The expectations regarding lab work and reporting are described in a separate document,‘KNE351. FLUIDMECHANICS: Laboratory Method and Reporting’, which will also be circulated at the beginning of the course. It is expected that all students study these notes and complete the pre-lab component prior to the laboratory session. An overview of the laboratory equipment will be provided at the beginning of each session.

A D Henderson

2

1. Learning Objectives

1. Observe and understand the behaviour of a real fluid flowing over a broad-crested weir,

2. Model this behaviour employing the Continuity and Bernoulli (Energy) Principles to predict the flow rate from depth measurements.

3. Evaluate these predictions by comparing with measured values and use Specific Energy

to explain the changing nature of the flow over the weir. 2. Introduction The theory of non-uniform flow in channels is covered by the course text, by many other fluid mechanics texts, and by several web sites. The specific energy, E, is the energy at a channel cross-section referred to the base of the channel (in contrast to the Bernoulli equation, which is referred to a fixed horizontal datum). The expression given for E is actually an approximation valid for small bed slopes. You've measured the flume slope, and should examine this approximation in your report. A hydrostatic pressure distribution is assumed, and you should also examine the validity of this assumption. If the streamlines are not parallel, then the accelerative forces will modify the pressure - depth relationship. In general, two conjugate flows depths satisfy the specific energy equation for a given value of the specific energy. The greater depth is associated with subcritical flow, and the shallower depth with supercritical flow. At the critical depth the conjugate depths are equal, and the discharge for the given specific energy is a maximum. Broad crested weirs are used as a method of flow measurement in open channel flows. If the weir is sufficiently high and long, the free surface will drop to critical depth. If the height of the upstream flow is measured, then the flow rate can be determined.

3

3. Apparatus • Water flume comprising of pump, control valve, venturi and v-notch flow meters,

downstream control gate. • depth gauges • 2 vertical water manometers • 2 total head tubes

4. Preparation Examine and sketch the layout of the channel and associated flow measuring equipment. Measure the channel width and note significant geometrical parameters of the nozzle venturi meter and V-notch weir. Note the directions of readings of all measuring scales.

a. Measure the channel, weir dimensions, and v-notch angle.

b. Take zero readings for the manometers.

c. Prime the pump. Fill the flume and the v-notch weir (slowly) and take a zero reading. 5. Measurement of Channel Slope and Point Gauge Traverse Rails. The horizontal datum line provided by a still water surface can be used to determine the channel bed slope and identify any departures from linearity in the channel bed or point gauge traverse rails.

a. Raise the gate and seal the edges with placticine. b. Start the motor and run about 100 mm depth of water into the channel. Close the valve

and stop the motor. c. When the water surface is still, take a series of point gauge readings on the water

surface at horizontal intervals of about 0.25 m over the whole length of the channel. Repeat this for the channel bed and aim for a precision of 0.2 mm.

6. Detailed Measurements of Free Surface Profile at Two Flow Rates

a. Lower the downstream gate all the way, open the control valve, and obtain a high flow rate by opening the control. Note you should have a region of critical flow where the depth is approximately constant on the weir crest. If this is not the case, reduce the flow rate.

b. Position the total head tubes adjacent to each other in the flow to verify they measure equal pressure (no head loss). Note that the reading is unchanged by probe position.

c. Position the total head tubes upstream and downstream from the weir (carefully to keep them submerged). You should observe a small loss of total head over the weir.

d. When the water level stabilizes, measure the water surface over the weir using the pointer gauge. Also measure the upstream depth and some 5 – 7 downstream depths over the weir until the flow depth is approximately constant. Record manometer readings and v-notch readings.

e. Repeat the experiment with approximately half the flow height over the weir crest (note that H/Lw should be > 0.08 to avoid viscous effects.

4

7. Effect of Downstream Condition on Flow

a. Slowly raise the height of the downstream gate in about 5 steps until the weir ‘drowns’, and the upstream depth begins to change. At each gate setting, record the manometer readings, v-notch readings, the upstream depth (at one point upstream where H stops changing), and the downstream depth (one point only). Detailed surface profiles are not required.

b. Close the control valve and turn off the pump.

8. Analysis

a. Correct your measured profiles for variations in point gauge traverse rails b. Plot the two water surface profiles over the weir. c. There are four ways of estimating flow rate. First, use the venturi and v-notch manometer

measurements to calculate the flow rate. d. Compare these values with the expected flow rate from the formula in your prelab

calculations – note the discharge coefficient will not apply in this case because the weir has a smooth profile with low losses.

e. Estimate the flow rate assuming that critical conditions were observed on the weir crest. f. Calculate the critical depth for the actual flow rate and plot this location on your water

surface profile. g. Calculate the Specific Energy for each measurement point based on the actual flow rate

and measured water depth and plot Specific Energy against depth. h. Calculate the Froude No. for each measurement point. Plot Froude number vs distance. i. From the total head measurements (total energy expressed in m of water) upstream and

downstream of the weir, calculate the head (energy) loss across the weir for the different gate positions.

9. Discussion

a. Locate critical depth and label the sub-critical, critical and super-critical flow regimes (giving Froude Numbers) on your water surface profiles.

b. Compare your ideal and actual flow rates. c. Does the flow gain or lose momentum as it passes over the weir? Explain. d. Does the flow gain or lose energy as it passes over the weir? Explain. e. What is a flow control? f. What happens to the flow over the weir when the tail gate is raised? Explain why

upstream head remains unchanged while the weir flow is not submerged? g. When is the head loss across the weir greatest? Explain why. h. Errors between experiment and theory have 3 possible sources;

i. inadequate theory (assumptions violated), ii. errors in experimental measurement,

iii. calculation errors. Which do you think are most significant in your experiment, and why?

5

6

7

8