#### Why head loss is same in parallel pipes

The basic approach to all piping systems is to write the Bernoulli equation between two points, connected by a streamline, where the conditions are known. For example, between the surface of a reservoir and a pipe outlet. The total head at point 0 must match with the total head at point 1, adjusted for any increase in head due to pumps, losses due to pipe friction and so-called "minor losses" due to entries, exits, fittings, etc. Pump head developed is generally a function of the flow through the system, with head rise decreasing with increasing flow through the pump.

Friction losses are a complex function of the system geometry, the fluid properties and the flow rate in the system. By observation, the head loss is roughly proportional to the square of the flow rate in most engineering flows fully developed, turbulent pipe flow. This observation leads to the Darcy-Weisbach equation for head loss due to friction:.

Thus, it is often useful to estimate the relationship as the head being directly proportional to the square of the flow rate to simplify calculations. Reynolds Number is the fundamental dimensionless group in viscous flow.

Velocity times Length Scale divided by Kinematic Viscosity. Relative Roughness relates the height of a typical roughness element to the scale of the flow, represented by the pipe diameter, D.

Pipe Cross-section is important, as deviations from circular cross-section will cause secondary flows that increase the pressure drop.

Non-circular pipes and ducts are generally treated by using the hydraulic diameter. For laminar flow, the head loss is proportional to velocity rather than velocity squared, thus the friction factor is inversely proportional to velocity.

The Reynolds number must be based on the hydraulic diameter. Blevins Applied Fluid Dynamics Handbook, tablepp. For turbulent flow, Colebrook found an implicit correlation for the friction factor in round pipes. This correlation converges well in few iterations. Convergence can be optimized by slight under-relaxation. From Q and piping determine Reynolds Number, relative roughness and thus the friction factor.

Substitute into the Darcy-Weisbach equation to obtain head loss for the given flow. Substitute into the Bernoulli equation to find the necessary elevation or pump head.

Pipes in Parallel (Tutorial 9)

Obtain the allowable head loss from the Bernoulli equation, then start by guessing a friction factor. Calculate the velocity from the Darcy-Weisbach equation. From this velocity and the piping characteristics, calculate Reynolds Number, relative roughness and thus friction factor. Repeat the calculation with the new friction factor until sufficient convergence is obtained. Although they often account for a major portion of the head loss, especially in process piping, the additional losses due to entries and exits, fittings and valves are traditionally referred to as minor losses.

These losses represent additional energy dissipation in the flow, usually caused by secondary flows induced by curvature or recirculation. The minor losses are any head loss present in addition to the head loss for the same length of straight pipe.

Like pipe friction, these losses are roughly proportional to the square of the flow rate. Defining K, the loss coefficient, by. K is the sum of all of the loss coefficients in the length of pipe, each contributing to the overall head loss. Although K appears to be a constant coefficient, it varies with different flow conditions. Factors affecting the value of K include:. Some very basic information on K values for different fittings is included with these notes and in most introductory fluid mechanics texts.

For more detail see e. Blevins, pp. To calculate losses in piping systems with both pipe friction and minor losses use. The procedures are the same except that the K values may also change as iteration progresses.Major Loss: It is calculated by Darcy Weisbach formulas.

Loss of head due to friction. For turbulent flow, coefficient of friction. Mean velocity of flow. Relation between Coefficient of Friction and Shear Stress. We get. Minor Loss: The another type of head loss in minor loss is induced due to following reasons. Loss due to Sudden Enlargement. Head loss. Loss due to Sudden Contraction. Head loss. Remember v 1 is velocity at point which lies in contracted section. Loss of Head at Entrance to Pipe. Loss at Exit from Pipe. Note: In case 1 and 2, flow occurs between pipe to pipe, while in case 3 and 4, flow occurs between tank and pipe.

We are taking entry or exit w. So, be careful. Combination of Pipes: Pipes may be connected in series, parallel or in both. Let see their combinations. Pipe in Series: As pipes are in series, the discharge through each pipe will be same. If minor loss are neglected then. Pipes in Parallel: In this discharge in main pipe is equal to sum of discharge in each of parallel pipes.

Loss of head in each parallel pipe is same. Equivalent Pipe: A compound pipe which consists of several pipes of different lengths and diameters to be replaced by a pipe having uniform diameter and the same length as that of compound pipe is called as equivalent pipe. Power Transmission through Pipe P. Power delivered by a given pipe line is maximum when the flow is such that one third of static head is consumed in pipe friction.

Thus, efficiency is limited to only Maximum efficiency. Water Hammer: When a liquid is flowing through a long pipe fitted with a vale at the end of the pipe and the valve is closed suddenly a pressure wave of high intensity is produced behind the valve.

This pressure wave of high intensity is having the effect of hammering action on the walls of the pipe. This phenomenon is known as water hammer.

Intensity of pressure rise due to water hammer.The pressure loss in the equations above can be substituted with a generic expression for pressure loss like the D'Arcy-Weisbach equation. Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro.

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## Worked Example 7: Parallel Pipes

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### Head Losses in Pipes, Bends and Fittings Notes for Mechanical Engineering

Privacy We don't collect information from our users. Citation This page can be cited as Engineering ToolBox, Pipes - in Series or Parallel. Modify access date. Scientific Online Calculator. Make Shortcut to Home Screen?This resistance is termed pipe friction and is usually measured in feet or metres head of the fluid, which is why it is also refered to as the head loss due to pipe friction. Head Loss in a Pipe. A large amount of research has been carried out over many years to establish various formulae that can calculate head loss in a pipe.

Three types of head loss occur in all pipes: entrance loss, exit loss, and loss through the pipes.

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In the setup head was loss through the bends, expansion and contraction. From the points we measured, we can neglect all these frictions expect for friction across the pipe. For example, it may be desired to predict the rate of flow along a proposed pipe connecting two reservoirs at different levels. Major Head Loss - Friction Loss - Nuclear Power In one word, Yes, the pressure difference will be same across the parallel combination, analogous to the same potential difference across the resistors in parallel combination.

This is the beauty of physics. These types of analogies help in better understanding, help to correlate concepts. Flow rate and pressure head - LinkedIn SlideShare 9. At constant flow rate and pipe length, the head loss is inversely proportional to the 4th power of diameter for laminar flowand thus reducing the pipe diameter by half increases the head loss by a factor of This is a very significant increase in head loss, and shows why larger diameter pipes lead to much smaller pumping power requirements.

The pressure head lost due to flow through pipes and other losses. It is very common in engineering and the calculations are done completely different as with series flow! In parallel Flow you got to keep in mind two.The head loss of a pipe, tube or duct system, is the same as that produced in a straight pipe or duct whose length is equal to the pipes of the original systems plus the sum of the equivalent lengths of all the components in the system.

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This can be expressed as. The major head loss for a single pipe or duct can be expressed as:. Since the velocity - v - in equation 2 in general is related to the pipe or duct where the component is located, the sum of the minor losses in a pipe or duct can be expressed as:.

The minor loss can be calculated by summarizing the minor loss coefficients - and multiplying the sum with the dynamic pressure head. The total head loss for a single pipe can be calculated by using equation 1 and 3 :. The total head loss in several serial connected pipes can be calculated by adding the total head loss in each pipe or duct.

The total head loss can be expressed as:. Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro. We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Minor Head Loss - head loss or pressure loss - due to components as valves, bends, tees and the like in the pipe or duct system. Tag Search en: major minor head pressure loss drop pipe tube duct systems. Privacy We don't collect information from our users. Citation This page can be cited as Engineering ToolBox, Modify access date. Scientific Online Calculator. Make Shortcut to Home Screen?Major Loss : It is calculated by Darcy Weisbach formulas. Loss of head due to friction.

For turbulent flowcoefficient of friction. Relation between Coefficient of Friction and Shear Stress. We get. Minor Loss:. The another type of head loss in minor loss is induced due to following reasons. Loss due to Sudden Enlargement. Head loss. Loss due to Sudden Contraction. Head loss. Remember v 1 is velocity at point which lies in contracted section. Loss of Head at Entrance to Pipe.

Loss at Exit from Pipe. Note: In case 1 and 2, flow occurs between pipe to pipe, while in case 3 and 4, flow occurs between tank and pipe. We are taking entry or exit w. So, be careful. Combination of Pipes: Pipes may be connected in series, parallel or in both. Let see their combinations. Pipe in Series: As pipes are in series, the discharge through each pipe will be same. If minor loss are neglected then.

Pipes in Parallel: In this discharge in main pipe is equal to sum of discharge in each of parallel pipes. Loss of head in each parallel pipe is same. Equivalent Pipe: A compound pipe which consists of several pipes of different lengths and diameters to be replaced by a pipe having uniform diameter and the same length as that of compound pipe is called as equivalent pipe. Power Transmission through Pipe P. Power delivered by a given pipe line is maximum when the flow is such that one third of static head is consumed in pipe friction.Log In.

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