Thursday, October 22

# Fluid mechanics pipe flow problems

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. The volume rate of flow through the pipes in series is the same throughout. Suppose a pipe line consists of a number of pipes of different sizes and lengths. See Fig. Let d 1d 2d 3 be the diameters of the component pipes. Let l 1l 2l 3 be the lengths of these component pipes.

Let v 1v 2v 3 be the velocities in these pipes. Pipes connected in continuation as in this case are said to be connected in series. In this arrangement the rate of discharge Q is the same in all the pipes. Ignoring secondary losses the total loss of head is equal to the sum of the friction losses in the individual pipes. Let d 1d 2d 3 be the diameters, and l 1l 2l 3 be the lengths of the various pipes in a series connection. Let Q be the discharge. Let h f be the total loss of head. Let d be the diameter of an equivalent pipe of length l to replace the compound pipe to pass the same discharge at the same loss of head. Equivalent Length of a Pipe with Intermediate Fittings :.

Pipes are said to be in parallel when they are so connected that the flow from a pipe branches or divides into two or more separate pipes and then reunite into a single pipe.

Suppose a main pipe branched at section into two pipes of lengths l 1 and l 2 and diameters d 1 and d 2 and unite again at a section to form a single pipe. In this arrangement the total discharge Q divides into components Q 1 and Q 2 along the branch pipes such that —.

In this arrangement the loss of head from section to section is equal to the loss of head in any one of the branch pipes. Hence the total discharge Q divides into components Q 1 and Q 2 satisfying the above equation. Similarly when a number of pipes be connected in parallel, then also, the total loss of head in the system is equal to the loss of head in any one of the pipes. For example in the arrangement shown in Fig.Energy is defined as ability to do work.

Fluid Mechanics: Minor Losses in Pipe Flow (18 of 34)

Both energy and work are measured in Newton-meter or pounds-foot in English. Kinetic energy and potential energy are the two commonly recognized forms of energy. In a flowing fluid, potential energy may in turn be subdivided into energy due to position or elevation above a given datum, and energy due to pressure in the fluid. Head is the amount of energy per Newton or per pound of fluid. Kinetic Energy and Velocity Head Kinetic energy is the ability of a mass to do work by virtue of its velocity. Velocity Head of Circular Pipes The velocity head of circular pipe of diameter D flowing full can be found as follows.

Elevation Energy and Elevation Head In connection to the action of gravity, elevation energy is manifested in a fluid by virtue of its position or elevation with respect to a horizontal datum plane. Pressure Energy and Pressure Head A mass of fluid acquires pressure energy when it is in contact with other masses having some form of energy.

Pressure energy therefore is an energy transmitted to the fluid by another mass that possesses some energy. The total energy or head in a fluid is the sum of kinetic and potential energies. Recall that potential energies are pressure energy and elevation energy.

Power is the rate of doing work per unit of time. Neglecting head lost, the total amount of energy per unit weight is constant at any point in the path of flow. Energy Equation Neglecting Head Loss Without head losses, the total energy at point 1 is equal to the total energy at point 2. No head lost is an ideal condition leading to theoretical values in the results. Energy Equation Considering Head Loss The actual values can be found by considering head losses in the computation of flow energy.

Energy Equation with Pump In most cases, pump is used to raise water from lower elevation to higher elevation. In a more technical term, the use of pump is basically to increase the energy of flow.

The pump consumes electrical energy P input and delivers flow energy P output. Energy Equation with Turbine Turbines extract flow energy and converted it into mechanical energy which in turn converted into electrical energy.

It is the line to which liquid rises in successive piezometer tubes.To browse Academia.

### Bernoulli's example problem

Skip to main content. Log In Sign Up. Pita Benavides. Fluid Flow in Pipes We will be looking here at the flow of real fluid in pipes — real meaning a fluid that possesses viscosity hence looses energy due to friction as fluid particles interact with one another and the pipe wall.

Recall also that flow can be classified into one of two types, laminar or turbulent flow with a small transitional region between these two. And hence how much energy must be used to move the fluid. The shear stress will vary with velocity of flow and hence with Re. Many experiments have been done with various fluids measuring the pressure loss at various Reynolds numbers. But for laminar flow it is possible to calculate a theoretical value for a given velocity, fluid and pipe dimension.

As this was covered in he Level 1 module, only the result is presented here. However analytical expressions are not available so empirical relationships are required those derived from experimental measurements.

Consider the element of fluid, shown in figure 3 below, flowing in a channel, it has length L and with wetted perimeter P. The flow is steady and uniform so that acceleration is zero and the flow area at sections 1 and 2 is equal to A. To make use of this equation an empirical factor must be introduced.

Assessment of the physics governing the value of friction in a fluid has led to the following relationships 1. An expression that gives f based on fluid properties and the flow conditions is required. Equation the two equations for head loss allows us to derive an expression of f that allows the Darcy equation to be applied to laminar flow. A rough pipe is one where the mean height of roughness is greater than the thickness of the laminar sub-layer. Nikuradse artificially roughened pipe by coating them with sand.

The regions which can be identified are: 1. Pipe flow normally lies outside this region 3. Smooth turbulent The limiting line of turbulent flow.

All values of relative roughness tend toward this as Re decreases. Transitional turbulent The region which f varies with both Re and relative roughness. Most pipes lie in this region. Rough turbulent.If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos.

Science Physics Fluids Fluid Dynamics. Volume flow rate and equation of continuity. What is volume flow rate? Bernoulli's equation part 1. Bernoulli's equation part 2. Bernoulli's equation part 3. Bernoulli's equation part 4.

Bernoulli's example problem. What is Bernoulli's equation? Viscosity and Poiseuille flow. Turbulence at high velocities and Reynold's number. Venturi effect and Pitot tubes. Surface Tension and Adhesion.

Current timeTotal duration Google Classroom Facebook Twitter. Video transcript Let's say I have a horizontal pipe that at the left end of the pipe, the cross-sectional area, area 1, which is equal to 2 meters squared. Let's say it tapers off so that the cross-sectional area at this end of the pipe, area 2, is equal to half a square meter. We have some velocity at this point in the pipe, which is v1, and the velocity exiting the pipe is v2. The external pressure at this point is essentially being applied rightwards into the pipe.

Let's say that pressure 1 is 10, pascals. The pressure at this end, the pressure that's the external pressure at that point in the pipe-- that is equal to 6, pascals. Given this information, let's say we have water in this pipe. We're assuming that it's laminar flow, so there's no friction within the pipe, and there's no turbulence. Using that, what I want to do is, I want to figure out what is the flow or the flux of the water in this pipe-- how much volume goes either into the pipe per second, or out of the pipe per second?

We know that those are the going to be the same numbers, because of the equation of continuity. We know that the flow, which is R, which is volume per amount of time, is the same thing as the input velocity times the input area.Recommend Documents.

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Fluid Mechanics Fluid Mechanics.Acoustic Flow Meter Design Calculator. Solve problems related to flow meters, average axial velocity of water flow, sensors, acoustic signal upstream and downstream travel time, acoustic path length between transducer faces and angle between acoustic path and the pipe's longitudinal axis. Bernoulli Theorem Calculator. Online script for solving any variable in the Bernoulli Theorem equation. Solve for head loss, static head, elevation, pressure energy, velocity energy, density and acceleration of gravity.

Assists in the computations for leak discharge, pipe networks, tanks, sluice gates, weirs, pilot tubes, nozzles and open channel flow. The flow is assumed to be streamline, steady state, inviscid and incompressible. Cauchy Number Calculator. Cavitation Number Calculator. Solve problems related to cavitation number, local pressure, fluid vapor pressure, fluid density and characteristic flow velocity. Chezy Equation Calculator. Solve problems related to Chezy equation, flow velocity, Chezy coefficient, roughness coefficient, hydraulic radius and conduit slope. Colebrook Equation Calculator. Solve problems related to Colebrook equation, turbulent flow, Darcy friction factor, absolute roughness and Reynolds number.

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## Questions & Answers – Fluid Mechanics

Online solver for any variable in the Darcy-Weisbach equation. Solve for head loss, friction factor, pipe diameter, pipe length, flow velocity and acceleration of gravity. Darcy's Law Equation Calculator. Solve problems related to flow rate, hydraulic conductivity, hydraulic gradient, solids volume, saturated soil phase diagram, flow cross sectional area, darcy velocity or flux, seepage velocity, voids effective cross sectional area, flow gross cross sectional area, pressure head, solids, porosity, void ratio and length of column.

Density Equations Calculator. Euler Number Calculator. Solve problems related to Euler number dimensionless value, fluid dynamics, pressure change, density and characteristic flow velocity. Fluid Pressure Calculator.

Solve for different variables related to force, area, bulk modulus, compressibility, change in volume, fluid column top and bottom pressure, density, acceleration of gravity, depth, height, absolute, atmospheric and gauge pressure.

Gravity Equations Calculator. Solves problems related to Newton's law of gravity, universal gravitational constant, mass, force, satellite orbit period, planet mass, satellite mean orbital radius, acceleration, critical speed, escape speed, radius from planet center and Kepler's third law. Hazen Williams Calculator.The figure on the left shows a simple Flowmaster network of a foul water pumping station, pumping to a treatment plant 10km away. The usual starting point for this and most hydraulic studies is to carry out a series of steady state analysis modelling the various flow scenarios.

Flow systems are not always steady state for instance when a pump starts or a valve opens the flow will change and the system has a transient response. However for many systems the transient response is not significant and so can be ignored.

The theory of flow in pipes and open channels is well documented. For a simple pipe system the analysis is relatively straightforward and the equations can be easily solved using a spreadsheet. For more complex systems such as networks a number of simultaneous equations need to be solved making a solution more difficult to find. Today there are a number of software tools designed to solve these flow problems such as Flowmaster and Wanda. A flow analysis can only be as accurate as the model that is used.

Errors usually occur in modelling fittings such as bends, tees, non-standard components and in determining appropriate roughness factors. Getting the model right and knowing that the results are correct comes with experience. Analysing the behaviour of pre designed systems may only confirm what you already know.

At Fluid Mechanics we have the necessary experience to offer a lot more. For new systems we can assist in the design process, providing recommendations on system design and control, optimise pipe and fitting sizing, provide performance specifications for pumps and valves and assist in supplier selection.

For existing systems we can assist in identification of problems and recommend solutions or improvements, for example how energy consumption can be reduced. This website uses cookies to improve your experience.