Fluid flow in pipes solved problems

Solved practical problems in fluid mechanics 1st edition. The fanning friction factor is dependent on a number of parameters related to the size of the pipe and the fluid, which can all be represented by another dimensionless quantity, the reynolds number re. Bernoullis equation is a special case of the general energy equation that is probably the most widelyused tool for solving fluid flow problems. The pipe flow problems described earlier can be solved by a method of successive trials that make use of eqs. Further we describe the fluid flow using differential equations for both types of the. In laminar flow, no m ixing occurs between adjacent lay ers and it occurs at low average velocities. In fluid dynamics, pipe network analysis is the analysis of the fluid flow through a hydraulics network, containing several or many interconnected branches. Consider a steady, incompressible boundary layer with thickness. A container filled with water and there is a hole, as shown in the figure below. The velocity of fluid flowing out from the capillary pipes is approximately proportional to the height of the fluid above the opening, that is \v kh,\ where \k\ is a certain constant depending on the fluid viscosity, geometry and material of the pipe. Two major areas of fluid mechanics applications in civil engineering are open channel flow and flow in pipes. Pdf hardy cross method for solving pipe network problems.

The volume rate of flow through the pipes in series is the same throughout. Viscous flow in pipes, laminar pipe flow characteristics 16 of 34. Once the fluid reaches the end of the entrance region, section 2, the flow is simpler to describe because the velocity is a function of only the distance from the pipe centerline, r, and independent of x the flow. Not only that, but these problems also provide the fundamentals behind the problem. We generally use pipes in our homes to supply water from water tank to kitchen, bathroom, etc. That shouldnt be too surprising since bernoullis equation. For more complex systems such as networks a number of simultaneous equations need to be solved making a solution more difficult to find. The flow of fluids in a pipe is widely studied fluid mechanics problem. The fluid the fluid typicallytypically enters the pipe with a enters the pipe with a nearly uniform nearly uniform velocity profile at section 1.

Fluid flow in tjunction of pipes university of vermont. Flow in pipes continued hydraulics and hydrologic systems. The manning equation is used for uniform open channel flow calculations including flow rate and normal depth. Pipes are said to be in series if they are connected end to end in continuation with each other so that the fluid flows in a continuous line without any branching. Fluidflow is easytouse and equips you with all the tools needed to design or analyze safe, reliable and energy efficient pipe flow. Based on the principle that many students learn more effectively by using solved problems, solved practical problems in fluid mechanics presents a series of worked examples relating fluid flow concepts to a range of engineering applications. For more complex systems such as networks a number of simultaneous equations need to be solved. Fluid mechanics problems for qualifying exam fall 2014 1.

The examples presented and their solutions are intended to present the possibility of calculator application in solving fluid flow problems in pipes. The solution of either of these problems typically requires an iterative approach. A pipe transmits water from a tank a to point c that is lower than water level in the tank by 4 m. For turbulent flow, if the velocity is unknown, equations 19.

This equation can be solved using and fluid flow regime calculator. The diameter of pipe is 15 cm for first 25 m from the tank, and then the diameter is suddenly enlarged to 30 cm. Fully developed flow 25 the fluid the fluid typicallytypically enters the pipe with a enters the pipe with a nearly uniform nearly uniform velocity profile at section 1. This book will help readers master every type of fluid mechanics and hydraulics problem that they in homework assessments tests and exams, from properties of fluids. This book will help readers master every type of fluid mechanics and hydraulics problem that they in homework assessments tests and exams, from properties of fluids to drag and lift. Bernoullis example problem video fluids khan academy. Fundamentals of fluid mechanicsfluid mechanics chapter 8 pipe.

A pipe, 40 m long, is connected to a water tank at one end and flows freely in atmosphere at the other end. Fluid mechanics calculations and example problems in civil. This is a common problem that arises especially in civil engineering where we have multiple pipes which are connected and possibly multiple fittings such as accoutrements, valves, etc. Water in a city is distributed by extensive piping networks. In direction of flow, due to friction cause by viscosity of the fluid we have v2. Pipe network analysis hardycross method determine the flow distribution in the pipe. When a fluid flows through a pipe or over a solid object, the velocity of the fluid varies depending on position. Define the rate of flow rate of flow for a fluid and solve problems using velocity and cross section. As the fluid moves through the pipe, viscous effects cause it to stick to the pppipe wall the no slippy boundary condition. Another alternative for pipe flow calculations is the hazen williams equation for. Consider liquid, gas, twophase, slurry or nonnewtonian fluids from a single solution. Hardy cross method for solving pipe network problems.

For problems requiring determination of the diameter, a trial. Constant velocity is shown by equidistant spacing of parallel streamlines as shown in figure 7. Jul 28, 2012 the first part of our first example regarding turbulent pipe flow and using the darcyweisback equation. Fundamentals of fluid mechanicsfluid mechanics chapter 8. The manometer shows a difference in head of 5 cm of water. Explain and solve problems involving laminar flow though pipes and. Flow rate is the volume of fluid moving past a point per unit time. Assuming that the base state is one in which the fluid is at rest and the flow.

Perhaps the most extensive characterizations of pipe flow turbulence are those of laufer 162, bakewell et al. Sal solves a bernoullis equation example problem where fluid is moving through a pipe of varying diameter. In many cases the physics is the same for wall layers in pipe flow as for boundary layers. One way of representing variation in velocity is streamlines, which follow the flow path. A viscous liquid steadily exits a circular vertical pipe with inner diameter d with a parabolic velocity distribution see. As the fluid moves through the pipe, viscous effects cause it to stick to the pppipe wall the no slippy boundary condition 12. Example problems in solving lqequations vii hardy cross method 61 62 64. In typical pipe flow problems, we know the nature of the fluid that will flow through. Write and apply bernoullis equation s equation for the general case and apply for a a fluid at rest, b a fluid at constant pressure, and c flow through a horizontal pipe. Based on a control volume analysis for the dashed box, answer the following. Alaa elhazek 48 chapter 7 flow through pipes 71 friction losses of head in pipes 72 secondary losses of head in pipes 73 flow through pipe systems 71 friction losses of head in pipes.

It provides an easy way to relate the elevation head, velocity head, and pressure head of a fluid. The theory of flow in pipes and open channels is well documented. In fluid flow, it is convenient to work with an averagevelocity vavg, which remains constant in incompressible flow when the crosssectional area of the pipe. Consider a fluid that is flowing in a pipe, in which the pressure loss for ft of pipe is 100 kpa. Fluid dynamics problems and solutions solved problems in. These equations are of course coupled with the continuity equations for incompressible flows. This is a common problem that arises especially in civil engineering where we have multiple pipes which are connected. The correlations for entry length and pressure drop are available in terms of ow reynolds number. Pipeline fluid flow an overview sciencedirect topics. Chapter 11 covers steady pipe flow, chapter 12 covers steady open channel flow, chapter introduces the method of characteristics for solving waterhammer problems in unsteady pipe flow, and chapter 14 builds upon material in chapter by using characteristics to attack the more difficult problem of unsteady flow. Calculate the discharge and mean velocity at the outlet profile see fig. Flow in pipes is considered to be laminar if reynolds number is less than 2320, and turbulent if the reynolds number is greater than 4000. Based on the principle that many students learn more effectively by using solved problems, solved practical problems in fluid mechanics presents a series of worked examples relating fluid flow.

From the lower end of the pipeline water flows out to the. Force exerted by a flowing fluid on a pipe bend problem 2. The darcy weisbach equation is used along with the friction factor for pipe flow calculations. Studies will be made on how to express losses caused by a change in the cross sectional area of a pipe, a pipe bend and a valve, in addition to the frictional loss of a pipe. Plot the system head and pump head against flow and find the matching point. There are many types of losses of head for flowing liquids such as friction, inlet and outlet losses. Basic hydraulic principles of openchannel flow by harvey e. And for pressure continuity at point b, the frictional head loss between a and b in both pipes. Determining the pressure drop when the the pipe length and diameter are given for a speci. Students of classical fluid mechanics have routinely been taught how to use the moody chart to solve pipe flow problems.

This happens in a very short distance from the exit, so that gravity force is negligible. To download the notes i use for these videos, please click the following link. This effective problemsolver provides more than 2,500 solved fluid problems, which are fully solved stepbystep. The aim is to determine the flow rates and pressure drops in the individual sections of the network. Friction in pipe flow the classic approach the bernoulli equation, also known as the mechanical energy balance, is the basis for understanding flow in pipes. On a circular conduit there are different diameters. Difference diameters, equations and solved problems. Height of water in the tank is 8 m above the centre of pipe. Tjunction, head loss, navierstokes equation,kappa epsilon model. The delivery pipe is 30 m long, 100 bore diameter and has a friction coefficient of 0. Three different types of fluid flow are written in brief under. This article introduces a novel approach for the direct noniterative solution of such problems.

The manometer shows a difference in head of 5 cm of. For fluid flow in pipes, friction is described by a dimensionless number, the fanning friction factor f. The region of flow near where the fluid enters the pipe is. For a simple pipe system the analysis is relatively straightforward and the equations can be easily solved using a spreadsheet. The head loss that occurs in the components of a flow. Want to see more mechanical engineering instructional videos. The two key expressions are from section 9 i, firstly that the flow in equals the flow out, so we can say. Pressure loss differences for laminar vs turbulent flow. If a fluid is flowing in the round pipe of diameter d at the average flow. Losses by pipe friction let us study the flow in the region where the velocity distribution is fully developed after passing through the inlet region as shown below. Assume q1 and q2 are the discharges through the pipes 1 and 2 1 2q q q 8.

Pipe flow the solution of pipe flow problems requires the applications of two principles, the law of conservation of mass continuity equation and the law of conservation of energy bernoullis equation 1. Schaums 2500 solved problems in fluid mechanics and. Flow coefficient qnd3 constant q2 q2 n1n2dd23 q2 600900 5005503 0. Force exerted by a flowing fluid on a pipe bend problem 1 duration. May 04, 2014 types of fluid flow problems in design and analysis of piping systems, 3 problem types are encountered.

Apr 16, 2016 flow through pipe in parallel many times the flow from one reservoir to another reservoir is increased by connecting number of pipes in parallel as shown in fig. Each example was solved using a calculator and the example solution shown was obtained by simply entering known quantities into the calculator, selecting units of measure and type of calculation. In a pipe these lam inar lay ers are cy lindrical and m ay be called stream tubes. Fluid flow in tjunction of pipes the topic of this masters thesis was approved by the department council of the department of information technology on 16 january 2007. The pump impeller is 500 mm diameter and revolves at 600 revmin. The head loss that occurs in pipes is dependent on the flow velocity, pipe length and diameter, and a friction factor based on the roughness of the pipe and the reynolds number of the flow. Laminar and turbulent flows critical reynolds number recr for flow in a round pipe re 4000. Fluid flow in tjunction of pipes masters thesis 2007 61 pages, 39. Now consider two different scenarios where the original volumetric flowrate is doubled.

To download the solution of the following problem in pdf format, click here. The fluid velocity in a pipe changes from zeroat the surface because of the noslip condition to a maximum at the pipe center. The last topic i want to cover on flow in pipes is flow in pipe networks. If acceleration due to gravity is 10 ms2, what is the speed of water through that hole. Sep 12, 2016 pipes are circular in cross section area, identical to the shape of a roll of paper towels. In terms of crosssectional area and flow speed, the volume flow rate is. Fluid flow theory in order to complete this tutorial you should already have completed level 1 or have a good basic knowledge of fluid mechanics equiva lent to the engineering council part 1 examination 103. This increased surface roughness results in a larger pressure drop which requires more pumping energy to move the fluid compared to a new pipe. Visit the cal poly pomona mechanical engineering departments video library. When you have completed this tutorial, you should be able to do the following. Froehlich abstract the three basic principles of openchannelflow analysis the conserva tion of mass, energy, and momentum are derived, explained, and applied to solve problems of openchannel flow.

Force exerted by a flowing fluid on a pipe bend problem. When solving homework problems, use the values given in table. The first part of our first example regarding turbulent pipe flow and using the darcyweisback equation. The hot and cold water that we use in our homes is pumped through pipes.