# Flow Through Pipes: Major and Minor Losses

By Mukul Yadav|Updated : December 26th, 2022

In the "Flow through pipes" topic, we will understand the different flow characteristics when the flow occurs into the pipes. Based on these characteristics of flow through pipes, flow can be categorized into the laminar flow and turbulent flow. In this chapter, different losses that occurred in the pipe flow will be estimated.

### Flow Through Pipes PDF

The energy at the exit point is calculated based on the different losses in the pipe flow. These losses that occur during the flow through pipes are broadly classified into major types of losses and some minor losses. This article contains basic notes on the "Flow through pipes" topic of the "Fluid Mechanics & Hydraulics" subject.

## What is Flow Through Pipes?

Flow through pipes is an important topic in fluid mechanics. It is important to understand the different types of losses that occur during the flow through pipes for the GATE CE exam. Based on different losses, the total energy at the exit point of the pipe is calculated. ## Major Losses in Flow Through Pipes

In flow through pipes, losses that occur in the pipe flow are a very important parameter for the design. These losses include the major loss due to friction and some minor losses. Darcy Weisbach's equations can calculate major losses in flow through pipes. These are explained as follows.

Loss of head due to friction

hf = 4fLv2/2gd

where,

• L = Length of pipe,
• v = Mean velocity of flow
• d = Diameter of pipe,
• f = Coefficient of friction

or hf = f'Lv2/2gd

f' = 4f

friction factor for laminar flow, f = 64/ Re

Coefficient of friction, f = 16/ Re

For turbulent flow, the coefficient of friction

f = 0.079/(Re)0.25

Chezy’s Formula: In fluid dynamics, Chezy’s formula describes the mean flow velocity of steady, turbulent open channel flow. v= c √mi, c= Chezy's Constant = √(8g/f)

Relation between Coefficient of Friction and Shear Stress We get

f = 2τ0/ρv2

where,

• f = Coefficient of friction
• τ0 = Shear stress

## Minor Losses in Flow Through Pipes

Another type of head loss, minor loss, is induced for the following reasons. These losses are used in the GATE CE question paper to create the NAT-based questions.

### Loss due to Sudden Enlargement

Head loss, hL = (v1 - v2)2/ 2g

### Loss due to Sudden Contraction

Head loss, hL = 0.5 v22/ 2g

Remember, v2 is the velocity at a point in the contracted section.

### Loss of Head at Entrance to Pipe

hL = 0.5V21/2g

Loss at Exit from Pipe

hL = V21/2g

## Combination of Pipe Connections

Pipes may be connected in series, parallel or in both. Let's see their combinations.

Pipe in Series: As pipes are in series, the discharge through each pipe will be the same. Q = A1v1 = A2v2 = A3v3

Total loss of head = Major loss + Minor loss

H = hL1 + hL2

due to friction in each pipe

hL1 = hf1 + hf2 + hf3

While, minor loss = Entrance loss + Expansion loss + Contraction loss + Exit loss If minor losses are neglected, then, Pipes in Parallel: In this, discharge in the main pipe is equal to the sum of discharge in each parallel pipe. Hence, Q = Q1 + Q2

The head loss in each parallel pipe is the same,

hf1 = hf2

where hf1 and hf2 are head loss at 1 and 2, respectively.

Equivalent Pipe: A compound pipe with several pipes of different lengths and diameters to be replaced by a pipe with a uniform diameter and the same length as a compound pipe is called an equivalent pipe. (where, L = L1 + L2 + L3)

If f = f1 = f2 = f3

Then, Hydraulic Gradient Line (HGL) and Total Energy Line (TEL) HGL → It joins the piezometric head ((p/ρg) + z) at various points.

TEL → It joins the total energy head at various points:

{((p/ρg) + z) + (v2/2g)}

Note: HGL is always parallel but lower than TEL.

## Power Transmission Through Pipe (P)

When a pipe is connected to a water tank, Power applied by a pipe flow at the outlet end depends upon the flow characteristics, pipe characteristics, etc. It will be explained below in detail for different cases. Pideal = ρgQH

Pactual = ρgQ(H - hf); hf = head loss

Efficiency, η = (H - hf)/H

Power delivered by a given pipeline is maximum when the flow is such that one-third of the static head is consumed in pipe friction. Thus, efficiency is limited to only 66.66%

Maximum efficiency, ηmax = H/3.

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

The intensity of pressure rise due to the water hammer

P = -ρLν/t

When the valve is closed gradually, when valve closes suddenly with a rigid pipe.

P = ν × (Kρ)0.5

When the valve closed suddenly with a plastic pipe

ρ = ν ×[ρ/{(1/K) + (D/Et)}]0.5

If the time required to close the valve

t > 2L/C ⇒ Valve closure is said to be gradual.

t < 2L/C ⇒ The valve closure is said to be sudden.

Where,

• L = Length of pipe
• D = Diameter of pipe
• C = Velocity of pressure wave produced due to water hammer = √(K/P)
• v = Velocity of flow
• K = Bulk modulus of water
• E = Modulus of elasticity for pipe material.
• t = Time required to choose the valve.
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## Flow Through Pipes FAQs

• Flow through pipes means the study of the flow characteristics when it occurs in a pipe. During the flow through pipes, an external source of energy is always required to flow because in such conditions flow is occurring under the energy gradient.

• During the flow through pipes, flow can be laminar type, turbulent type, or transition type of flow. These flows can be classified based on the Reynolds number of the flow, which depends on the flow and pipe characteristics.

• Losses can be classified as major and minor during the flow through pipes. Major losses occurred in the pipe flow due to friction occurring at the wall of the pipes. And minor losses occur due to sudden contraction, expansion, exit, entrance, etc.

• In the case of flow through parallel pipes, head loss occurs between both ends of the flow is the same for the different parallel combinations of pipes. In such conditions of flow through pipes, total discharge is the sum of the discharges through the different pipes.

• Minor losses occurred in the flow through pipes consisting of loss due to sudden contraction, loss due to sudden expansion, entrance loss, exit loss, etc. these losses have less contribution to the total loss occurred in the flow.

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