Junction Loss Experiments: Laboratory Report
Junction Loss Experiments: Laboratory Report
Alternative Text
Figure 2. Diagram. Crosssection definition sketch of an access hole. This drawing shows a crosssectional view of three components of an access hole: a nonsloping inlet pipe on the lower left, which connects to an access hole in the center with a bottom but no top (or lid), which is connected to a nonsloping outlet pipe on the lower right. Arrows in the inlet pipe depict flow coming into the access hole with a velocity labeled V subscript i. Above the inlet pipe and next to the access hole it shows a line that slopes gently down to the right, which is labeled Hydraulic Grade Line. The location of the hydraulic grade line just outside the left side of the access hole coincides with the water level (also depicted as a blue line) shown inside the access hole. Above the hydraulic grade line is another line, which is almost parallel to it and is labeled Energy Grade Line.
The water level inside the access hole rises slightly as one moves toward the right side of the access hole. This vertical distance between the hydraulic grade line and the water surface on the left side of the access hole is labeled V subscript i superscript 2 divided by the product of 2 and g (gravity). The flow of water in the upper part of the access hole is depicted with thin lines as a clockwise swirl near the right side of the access hole, below the highest part of the water level. The flow depicted along the bottom of the access hole shows relatively horizontal flow lines that begin near the inlet pipe and end near the outlet pipe.
There are also flow lines depicted in the outlet pipe. These flow lines are mostly horizontal, except for a small clockwise swirl near the top of the flow just inside the outlet pipe. This area of the outlet pipe is circled and the depth of the flow below the swirl is labeled A subscript c. Below the outlet pipe a label says 3D P I V to measure contracted area (A subscript c). The hydraulic grade line above the outlet pipe is depicted with a line that lowers slightly, then increases slightly to a point directly above the swirl in the outlet pipe, and then gradually slopes downward to the right. Above the hydraulic grade line, the distance between the energy grade line on the immediate left side of the access hole and the energy grade line on the immediate right side of the access hole is labeled Inflow Loss (H subscript L, i). The energy grade line on the right side of the access hole is depicted with a line that slopes down pretty rapidly until immediately after the swirl in the outlet pipe (below), after which the energy grade line parallels the hydraulic grade line (below it). The drop in the energy grade before it parallels the hydraulic grade line is labeled Outflow Loss (H subscript L, o). The sum of the inflow loss and the outflow loss is labeled Total Energy Loss. The distance between the energy grade line and hydraulic grad line on the right side of the diagram is labeled V subscript o superscript 2 divided by the product of 2 and g (gravity).
Figure 3. Diagram. Flow chart for the proposed junction loss method. This flow chart is composed of a series of text boxes with labels and formulas in each of them. On the left side there are three text boxes with arrows between them that successively point to the text box below it. The top box on the left side is labeled Initial A H water depth. Right below this label is the formula: E subscript a1 equals the maximum of E subscript a, f f, E subscript a, i c s, and E subscript a, i c u. The middle text box on the left side is labeled Adjustments for Benching, Angled Inflow, and Plunging Inflow. Right below this label is the formula: E subscript a equals E subscript a 1 plus delta E subscript B plus delta E subscript Theta plus delta E subscript H. The bottom text box on the left side is labeled Inflow Pipe Exit Loss. Right below this label is the formula: E subscript i equals E subscript a plus delta E subscript i.
Each of the three text boxes on the left side has text boxes on their right that specify the Access Hole Parameters that are needed to compute the final quantity in the formula on the left side of the diagram. The text box labeled Initial A H water depth has the following three text boxes pointing to it. The first text box is labeled Full Flow and has the formula: E subscript a, f f equals y subscript o plus the quantity, P subscript o divided by gamma (specific weight), plus the quantity, V subscript o superscript 2 divided by the product of 2 and g, plus delta E subscript o c equals K subscript o times the quantity, V subscript o superscript 2 divided by the product of 2 and g. The second text box is labeled Inlet Control: Submerged and has the formula: E subscript a, i c s equals 1.0 times the squared quantity, Q divided by the product of A and the square root of g times D subscript o, times D subscript o. The third text box is labeled Inlet Control: Unsubmerged and has the formula: E subscript a, i c u equals 1.6 times D subscript o times the following quantity to the 0.67 power, Q divided by the product of A times the square root of g times D subscript o.
The text box labeled Adjustments for Benching, Angled Inflow, and Plunging Inflow has an Access Hole Parameters text box pointing to it that contains the formula: delta E subscript i equals C subscript i times the difference between Y subscript a 1 minus the sum of three terms: y subscript o plus P subscript o divided by gamma plus V subscript o superscript 2 divided by the product of 2 and g, where i equals B or theta or H. This text box then has the following three text boxes pointing to it, all within the Access Hole Parameters region of the diagram. The first text box is labeled Benching and has the formula: C subscript B, right arrow, H E C22. The second text box is labeled Angled Inflow and has the formula: C subscript theta equals 4.5 times the magnitude of the cosine of the quotient of theta subscript w divided by 2, times the quotient of the summation of Q subscript j divided by Q subscript o, where theta subscript w equals the quotient of the summation of Q subscript j times theta subscript j divided by the summation of Q subscript j. The third text box is labeled Plunging Inflow and has the formula: C subscript H equals the quotient of the summation of Q subscript k times H subscript k divided by the summation of Q subscript o, where H subscript k equals the quantity, z subscript k minus y subscript a 1, divided by D subscript o.
Finally, the text box labeled Inflow Pipe Exit Loss has a text box from the Access Hole Parameters region pointing to it. This text box has the formula: delta E subscript i equals K subscript i times V subscript i superscript 2 divided by the product of 2 and g.
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