Hardy-Cross Method Looped Method 2. Finally sum up all the moments, allotted moments, moments carried forward — at the end points of each member and rigid-end moments. As long as the last few iterations are done with attention to detail, the solution will still be correct. For loop 2-3-4, the change in flow is positive so its absolute value is applied in the counter-clockwise direction. The flow rates and pressure heads must satisfy the continuity and energy equations.
You can use your right and left arrow keys to scroll to the left and right to see the velocity in each pipe. If the method is followed correctly, the proper flow in each pipe can still be found if small mathematical errors are consistently made in the process. The H,V,Re output field is scrollable using the left and right arrow keys on your keyboard. The Hardy Cross Method 15 The earliest systematic method of network analysis Hardy-Cross Method is known as the head balance or closed loop method. How long can that fire flow be provided for? Introduction Perfect structural breakdown of large unbreakable concrete building structures in the 1950s was a difficult mission, but we need to pay tribute to the engineering profession as well as to Hardy Cross, for very few failures. Enter a diameter of 0. Parallel feeder mains are cross connected at intervals of one to two kilometers, with valves to permit isolation of sections in case of a main break.
Retain sign from step a and compute sum for loop Σ hf. Check the node flow rates that you entered. For example, there is a 100-m long 10-cm diameter inside diameter pipe with one fully open gate valve and three regular 90 o elbows. Applications of Pipe Networks The pipe network analsyis calculation has many applications. If you are designing a pipe network as opposed to analyzing a pipe network that is already in place , vary the pipe diameters until the pipe velocities are reasonable and pressure at node D is as low as possible to minimize the height of the water tower.
Conservation of potential means that the total directional head loss along any loop in the system is zero assuming that a head loss counted against the flow is actually a head gain. Water Supply Network Design Analysis of water distribution system includes determining quantities of flow and head losses in the various pipe lines, and resulting residual pressures. The most crucial and functional part of the column is that it can be applied even to straight and bent beams. Darcy Weisbach or Hazen Williams losses Pipe Networks. Images Hardy Cross Method of Moment-distribution The achievements of Hardy Cross came at a time when engineers were struggling to apply the theory of elasticity, since it applies only to statically indeterminate structures. All fields must have a number, but the number can be 0. The next step is to find the product by multiplying the moment allocated to every member at a joint by the carry-over part found at the terminal of the member.
Clockwise head losses are from flows in the clockwise direction and likewise for counter-clockwise. A major water demand areas in a city should be served by a feeder loop; where possible the arterial mains should be laid in duplicate. Individual pipe lengths in the pipe network cannot exceed 10 7 m. Step 3:Write loop head-loss equations as where kn is total pipes in kth loop. The pipe length you should enter into the pipe network analysis calculator is 100 + 1. At the same time, it is too delicate and trouble-free to ignore. H,V,Re pipe: Topics for pipe network analysis: , , , Introduction to Pipe Networks Pipe network analysis simulates steady flow of liquids or gases under pressure.
Models are often used to optimize the design of new distribution systems or analyze major extensions or modifications to existing distribution systems. Enter one pressure in the pipe network and all other pressures are computed. Also known as piezometric head. The sum of pipe flows into and out of a node equals the flow entering or leaving the pipe network through the node. Divide network into number of closed loops.
Minor losses due to valves, pipe bends, etc. Enter the diameters and lengths of these pipes and the desired inflows at nodes A-H. Density and viscosity for the built-in fluids were obtained from Munson et al. Built-in fluid and material properties for pipe networks In the pipe network analysis calculator, the user may manually enter fluid density and viscosity or select one of the common liquids or gases from the drop-down menu. The method also assumes that the relation between flow rate and head loss is known, but the method does not require any particular relation to be used.
The procedure has to be repeated till the moments which are to be carried over become negligible. Normally, C will not exceed 150 and e will not exceed 0. If a subdivision or commercial development is built, will adequate pressures and flows exist? Let node I be the outflow from the pipe network and use all other nodes A-H as inflow locations; so flow is from node A through pipes 1, 2, 5, 7, 6, 8, 11, and 12 and out node I. Equations and Methodology for Pipe Networks The pipe network analysis calculation uses the steady state energy equation, Darcy Weisbach or Hazen Williams friction losses, and the Hardy Cross method to determine the flow rate in each pipe, loss in each pipe, and node pressures in the network. Please contact us for consulting or other questions about pipe networks. It allows students to analyze pipe distribution networks. You cannot have flow in or out of a node that is surrounded by non-existent pipes.
All of the arterials and secondary mains are looped and interconnected, eliminating dead ends and permitting water circulation such that a heavy discharge from one main allows drawing water from other pipes. Apart from this, the formulated method in figuring out undetermined binds was unwieldy, since it required as many simultaneous equations to be solved as there were redundancies in the structure. Now calculate the moments at the ends of the members of the frame. References for Pipe Networks Cross, Hardy. This software was designed for classroom use in hydraulics.