Advanced fluid mechanics

Course faculty:Dr . Khalil ahmad

Lab coordinator:Muhammad Adeel

Determination of Minor losses by using standard equipment

SEQUENCE1. Different types of Heads2. Reasons for loss of Heads3. Types of losses like Major Losses and Minor Losses4. How to determine Major losses5. Introduction to standard equipment used to determine Minor

losses6. How to determine Minor losses theoretically and practically7. Comparison between theoretical and practical values.

Different types of Heads

There are usually three types of Heads

Flow Head or Pressure Head (Pressure/unit weight) Elevation Head (Z) Kinetic Head/velocity head

Units of energy head is in the form of linear measurement

Reasons for loss of Heads

What do you think what is reason of loss of Energy head?

Can you tell difference between major losses and minor losses?What does Major & Minor dictates?How Minor losses can be produced in a pipe?

Determination of Major losses theoretically

Poiseuille's Equation For Laminar Flow Darcy weisbach equation Chezy equation for Head Loss

Introduction To Standard Equipment and Procedure

The equipment measures pressure drops at various flow rates when water flow through different pipe bends and fittings.

All bends and fittings are connected in series with pressure tapings on both sides of each device.

A water manometer with a vent valve and a hand air pump is connected to these tapings. A valve at the outlet is used to control the flow.

Front View

Backside view

ProcedureFollowing steps should be followed Before starting the test , place your instrument on Hydraulic Bench.

adjust leveling screws and connect water supply to bench outlet.

Procedure Start the Hydraulic Bench and adjust flow to about 20 lpm and adjust

test set flow control valve to remove all air from the piping system by purging.

Procedure

Adjust any discharge value through Hydraulic Bench. Adjust manometer level reading midrange by using

Flow control valve. Record this reading. By taking different discharge take more readings.

One thing to be noted isWhile moving from 1-2 portion , why there is increase in water manometer Head?

How to determine minor Head losses theoretically

We can calculate minor head losses step by step1-2 portion (Sudden expansion):There are two Head changes in this part.1. Head change (Gain) due to change in Diameter and its value can be

calculated by Bernoullis equation.H f = V12- v22/ 2g

2. Head Change (loss) due to sudden expansion and its value can be calculated by following formula

H f = ( V 1- V 2) 2 / 2g ( Equation 1) V 1= Velocity at contraction V 2= Velocity at dilation

Can you prove this equation?

HINT:You can prove this equation by using Bernoullis equation Momentum equations Equation of continuity

Determine V 1 and V 2 as you know Discharge through pipes and diameters of pipes.Pipe cross-section Diameter = 20 mmExpanded pipe cross section = 35mm

Compare calculated ( Theoretical ) values for Head loss and measured values for Head loss determined during Practical.

2-3 portion ( Sudden Contraction ):

There are two Head changes in this part.1. Head change (loss) due to change in Diameter and its value can be

calculated by Bernoullis equation.H f = V12- V22/ 2g

2. Head Change (loss) due to sudden contraction and its value can be calculated by following formula

H f = k V 22 / 2 g (Equation 2) Here K =[ 1 / Cc 1] and depending on D 2 / D 1 . Its values can be calculated from following table.

Can you prove this equation?

HINT:You can prove this equation by using Same equation 1 but by assuming that shape in which water

will enter contracted portion will be like that shape formed in dilated portion.

Equivalent Length of Bends & Fittings.

Energy loss in bends and fittings can not be expressed in definite formula as in pipe flow. However energy loss can be expressed as

H f = k V 22 / 2 gThat is why to determine losses across bends and fittings we use Equivalent length or K value of Bends and Fittings.Equivalent Length is length of straight and round pipe alongwhich loss of pressure head will be same as caused by the bend or fitting.

Procedure to determine Head loss across Bends and Fittings

Formula to determine Head loss will beH f = fLeV2/2Dg

f = Darcy-weishbach friction factor determine from Moody diagramLe = equivalent length determine from tableV = velocity determine by Q/ A of pipeD = diameter of pipeg = Gravitational constant

Moody Diagram Moody diagram is used to determine friction factor from relative

surface factor and reynolds no or product of velocity (m/s) and Diameter of pipe (cm). It is applicable only to Turbulent flow.

Relative roughness factorE/d factor is known as relative roughness factor.E= roughness of pipe material (mm)D = diameter of pipe (mm) =21mm

How to use Moody chartFirst determine relative roughness factor and draw a horizontal line onGraph. Lets suppose it is .007

How to use Moody chartThen determine either reynolds no or VD and draw a vertical line on Graph. Lets suppose it is 1.529 m/s cm.

How to use Moody chart Intersection of both lines will give us value of friction factor.

From 3-4 Miter 90 degree Now you can evaluate head loss across miter 90degree as you know all factors in formula H f = fLeV2/2Dgf = Darcy-weishbach friction factor determine from Moody

diagramLe = equivalent length determine from table = 3.8 ft

Compare this value with practical measured values

Head loss across small radius, large radius, 45 degree elbow and 90 degree elbow

Head loss across all these fittings can be determined by evaluating KFactor for each and comparing its value with reference values. K valuecan be evaluated by following formula

K= H f 2g/ V22H f = measured change in Head during practicalV2 = velocity of water through pipe (21mm)One thing to be noted is that during 6-7 portion 45 degree elbow measured head loss will be determined in such way H f67 = (H 6 H 7)While across other elements it will be determined like thisH f iL = (H i H L)

H I = initial Head H L = Last Head