## Appendix 3. Friction Losses and the Reynolds Number

The frictional head loss for fluids flowing in pipes is calculated by the following equation: (27) Where: f is the friction factor (see below for calculation) L is the pipe length (m) v is the average fluid velocity (m/s) D is the pipe diameter (m) g is the acceleration due to gravity (9.81 m/s/s) The only variable not available to us immediately is the frictional factor (f). This is dependent on the type of flow occurring in the pipe. There are basically two types of flow (although there is a transition state between them ), these are: Laminar flow. Example: This is similar to the stream of smoke from a cigarette in still air. Close to the cigarette the stream of smoke is very uniform and flowing evenly. This is laminar flow. Turbulent flow. Example: This is when the stream of smoke from the cigarette becomes unstable, with whorls and eddies. This state occurs in the stream of smoke after the laminar flow. These two states of flow can be described by a dimensionless quantity (just a number) known as the Reynolds Number (NRE). This number is calculated by the following formula: (28) Where: v is the average fluid velocity (m/s) D is the pipe diameter (m) μk is the kinematic viscosity of the fluid (m2/s), which is a measure of how ‘thick’ the fluid is If the Reynolds Number is less than 2000 then the fluid flow is laminar. In this case the friction factor (f) can be calculated by the following equation: (29) If the Reynolds Number is greater than 2000 then the fluid flow is turbulent. In this case the friction factor (f) can be calculated by use of a Moody...

Read More## Construction of a Gravity-fed Water Supply and Treatment System in Developing Countries

This paper covers every aspect of the design and construction of a water supply system utilizing potential energy (gravity) for delivery. The typical layout of a gravity-fed water system includes a water source, transmission main, reservoir and distribution system. Every component between the water source and the reservoir is discussed in this paper, which focuses on everything related to the transmission main. This includes pipeline route survey, water resource planning, pipeline design and pipeline construction. Water treatment systems are introduced and discussed briefly. For more information on these vital components of a water supply system, refer to the sources at the end of this paper for further reading. All calculations and measurements were done using the metric system. A large majority of communities that would find this information useful use the metric system. You can read the whole document as a PDF...

Read More## Distribution Network

In this system each family got their own tap that is connected to the reservoir tank using a polyethylene pipe network. The exit pipe work at the base of the reservoir. Making the tapstands. Fixing a t-joint into the distribution pipe work. A finished tap...

Read More## Fluid Mechanics For Gravity – Flow Water Systems and Pumps

A text detailing the design of water systems including the design parameters recommended for a successful and long lasting water supply. Issue 2 May 2003.

Read More## Gravity Flow Water Supply

By Santiago Arnalich Castañeda. This book intends to provide you with the tools needed to complete a sucessful gravity flow water project in a short amount of time. You may well already be dealing with a real life project, but without the time to do intensive study to get up to scratch. This book is meant to be: 99% Fat Free – Only what you really need is included. Simple – One of the most common causes of failure is that the complexity and excessive rigour become very intimidating, and things get left half done. Chronological – It more or less follows the logical order in which you’d undertake the project. Practical – With calculation examples. For a generous step by step exercises collection see “How to design a Gravity Flow Water System Through Worked Example“, a book from the same author. Self contained – It is assumed that you are in a remote area with not access to information, so all the essential information is included. Never the less links to other sources of information are provided. You can read the whole of Gravity Flow Water Supply on Google...

Read More## Natural Flow Calculator Spreadsheet

This spreadsheet allows the user to calculate the natural flow rate (LPS) of any combination of up to 4 pipes of different diameters (in) for given pipe lengths (m) and known head (m). Microsoft Excel Spreadsheet (165KB) *** Note: this spreadsheet contains macros, and you may get a security warning.

Read More## Part 5: Energy in a Perfect System – The Bernoulli Equation

Anywhere in a perfect system (i.e. there are no frictional effects), for an incompressible fluid there are three types of energy existing: Pressure Energy. Example: If you blow up the tyre of a car with a pump you are turning your physical energy of working the pump into pressure energy in the tyre. Kinetic Energy. Example: This is the energy contained in a moving fluid. If a wave hits you at the beach, you feel the kinetic energy contained within it. Potential Energy. Example: Gravity is trying to pull water to the lowest point on the earth’s surface. So when water is at a high point it contains energy, which can “potentially” allow it to flow down. At any point in a perfect system the sum of these “bits” of energy in different forms (Pressure, Kinetic and Potential) must equal the sum of these “bits” at any other point in the system. This is because energy cannot be “created” or “destroyed”, it can only change its form. This is what the BERNOULLI EQUATION expresses. Appendix 1. gives the derivation of the Kinetic Energy in terms of a pressure and Appendix 2. gives the derivation of the Potential Energy in terms of a pressure. These different forms of energy are expressed mathematically (as pressures) in the Bernoulli Equation (for a perfect system) shown below: (12) The terms on the left hand side of the Equation are as follows: P1 is the pressure energy at point 1 (expressed as a pressure). [Units are N/m2 or Pa] ρ is the density of the fluid.[Units are Kg/m3] v1 is the velocity of the fluid at point 1. [Units are m/s] g is the acceleration due to earth’s gravity (9.81 m/s/s).[Units are m/s/s] h1 is the height (from a given datum) of the fluid at point 1.[Units are m] The terms are similar on the right hand side of the Equation, but for point 2. The left hand side of the equation represents all the “bits” of energy (expressed as pressures) at a point 1 in a perfect system and the right hand side all the “bits” of energy (expressed as pressures) at another point...

Read More## Spring Tank

Water is taken from a spring, rather than the river, to reduce the risk of contamination by parasites and other pernicious micro-organisms. A tank is built at the spring to ensure a continuous head of water above the start of the mainline. Thus, the mainline should always run full without any air locks.This tank is cast from conctret and consists of a sedimentation area and a 380 liter tank. Making a mould out of wood into which the concrete will be poured. Positioning the spring tank mould at the spring. Rebar is added to the mould to provide reinforcement for the concrete. Concrete being poured into the spring tank mould. Concrete being compacted into the mould. Once the spring tank is finished a dam is cast around the spring. The spring tank and spring dam. Preparing the top of the spring tank so that the roof can be cast. Making the roof and entry hatch on top of the spring tank out of reinforced concrete. The finished spring tank. The pipe exiting from the spring tank where the valve box will be. Building a retaining wall above the spring. Constructing a mould so that the valve box can be cast. Making the valve box roof. Putting the finishing touches to the valve box roof. Water flowing from the spring through a pipe to the sedimentation area. The finished spring with the dam, spring tank and valve...

Read More## The Anatomy Of A Gravity Flow Water System

This section contains photographs that detail the construction of a gravity flow water system for 32 families. The system cost £130 per family and took 30 people 18 days to build. Before the system can be designed the area must be surveyed. The system consists of: A spring tank; A main pipeline, including a pipe bridge; A reservoir tank; A distribution network that leads to a tap at each house. For a gravity flow system to work properly the pipes must run full of water with no air locks. Gravity can then be used to move water, over hills and undulations, between the spring and the reservoir tank. This method works for as long as the spring tank is at the highest point in the system and that there is enough height difference, between the spring tank and the reservoir tank, to give a sufficient flow rate once friction losses have been taken into account. The distribution network also uses gravity to move water to the taps through thinner...

Read More## Water System Design Parameters

Condensed from A Handbook of Gravity-Flow Water Systems, Thomas D. Jordan Jnr., Intermediate Technology Publishing. It can be downloaded as a PDF. The following are a list of design parameters that are important in the design of gravity-flow water systems: Maximum Pressure Limits : The taps and valves closed state, should be the maximum pressure condition for the system. Maximum head limits for the pipe work will be used to carry out the calculations. This scenario is used at the start of the design to be able to place any break-pressure tanks that may be required. Safe Yield : The safe yield is the minimum flow from the water source. It is important to not draw more than this supply from the system at any point. If this happens then spring boxes and/or break pressure tanks will run dry and air will enter the system. Negative or Low Pressure Head : If the pressure head (P in the Bernoulli Equation) becomes negative at any point in the system then two things may happen. Firstly a siphon effect is occurring which is trying to suck water into the system. This is undesirable as polluted groundwater may be introduced into the system. Secondly, large negative pressures can cause air to come out of solution in the water and cause air-blocks. Jordan [P.52] suggests that the pressure head should, if possible, not fall below 10m (98100 Pa pressure) anywhere in the system and never go negative. Velocity Limits : The flow velocity in the pipelines should not be to great as particles suspended in the water will cause excessive erosion. Also if the velocity is too low then these particles will settle out of the flow and may clog the pipes at low points. This then requires washouts at low points in the system. Jordan [P.53] suggests that the minimum velocity should be 0.7m/s and the maximum 3.0m/s. Natural Flow : Natural Flow (see Section 8 i)) may be allowed to occur in the system at some sections of pipe. Natural flow can be problematic in that the water velocity may exceed the limits set in parameter 4 above and/or increase the flow rate above the safe yield parameter 2. Close attention should be made to these situations. Residual Head : The residual head at a tap stand or valve is important. If it’s too high it will cause erosion of the valve and if it is too low then the flow will be minimal. Jordan [P.141] suggests the following limits : Absolute minimum : 7m Low end of desired range : 10m Most desirable : 15m High end of desired range : 30m Absolute maximum : 56m Air-blocks : These occur when there are topographic features between the source and the collecting tank that are lower than the collecting tank. Energy is lost from the system as these air-blocks are compressed and can result in no flow. Jordan [P.55] gives the following design practices to avoid air-blocks : Arrange pipe sizes...

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