Engineering

In this article we will discuss about the relationship of Mass Flow Rate to Velocity.

The concept of flow rate(Mass Flow rate and Volume Flow Rate) measurement in a industry is very much essential for accurate and cost effective running of a process. Velocity indicates how fast a fluid is moving a distance per unit time.

Whenever we calculate flow rate of a fluid flowing through a pipe line certain terms like mass flow rate, volumetric flow rate, Molar flow rate, velocity, density, volume ,temperature , pressure etc come into the picture.

Flow rates and all the above mentioned physical properties are inter related and we can determine one quantity from the other by using different formulas associated with them.

Velocity=Distance traveled /Time

Volume Flow Rate, Q= Area x Velocity

Mass Flow Rate, ṁ=Density x Area x Velocity

Mass Flow Rate

Mass Flow Rate is the measurement of mass of a fluid passing through a passage per unit time.

Mass Flow rate can be expressed as,

ṁ=mass/time=m/t

SI unit of mass flow rate is Kg/s and it is denoted by ṁ.

Accurate measurement of Mass flow rate is necessary in an industry to control the different operations smoothly. Efficiency of an equipment and product quality also depends on mass flow rate of a fluid.

Mass is neither created nor destroyed and Mass flow rate is not affected by temperature and pressure change during the process so in case of precision measurement mass flow measurement is always advisable.

Mass Flow Rate to Velocity relationship

Flow rate measurement of different fluids is an important aspect of pipe line industries.

Velocity is the measurement of how fast a fluid is moving per unit of time. Mass Flow Rate is associated with the amount of fluid passing through a passage per unit time.

Mass Flow Rate can be expressed as ṁ=mass/time=m/t Eq1

And Volume Flow rate can be expressed as  Q= volume/time= V/t   Eq2

                                          From Eq(1), ṁ=mass/volume . volume/time Eq3

                                            Now, mass/volume=Fluid density ρ

                                            And volume/time=Volumetric Flow Rate=Q

                                             From Eq(3) , ṁ= ρ.Q         Eq4

The above equation relates Mass Flow rate and Volumetric Flow Rate of a fluid. If we know the density of the fluid and discharge through a pipe, then we can determine the amount of fluid passing through the pipe in terms of Kg/s i.e. mass flow rate of the fluid.

  From the Continuity Equation applicable for incompressible fluid we can write,

  Here A is the cross sectional area of the passage and bar(v) is the average velocity of the fluid.

 So Eq(4) becomes, 

From the Eq(5) it is clear that mass flow rate of a liquid is directly proportional to the density of the liquid, velocity of the liquid and the cross sectional area.

How to Calculate Mass Flow Rate from Velocity?

The Flow rates, velocity, pressure, density all these terms are interrelated to each other.

If we know the velocity(v)of a flow through a pipe of cross sectional area(A), then we can calculate the volume flow rate of the fluid by using following formula,

Where Q=Volume Flow rate

A= Cross sectional area of the pipe

= Average velocity of the fluid

Now Mass Flow Rate is the density ρ multiplied by the Volume Flow Rate

ṁ=ρ. Q or,

As per the law of conservation of mass, in case of incompressible fluid passing through a channel of non uniform cross sectional area, the Mass flow rate maintains a constant value.

In the above figure we can observe a pipe with different cross sectional area A1 and A2 (where A1>A2) through which water(incompressible in nature) is flowing.

Even though the diameter of the pipe is not same, due to continuity same amount of water is passing through the point 1 and 2. The speed of the fluid is less at the wider area of the passage than the speed at the narrow region to keep the flow constant. 

At point 1 and 2,

Q_{1}=Q_{2} or,

This is the famous Continuity Equation applicable for Incompressible fluids.

Difference between Mass Flow Rate and Velocity

The difference between Mass Flow Rate and Velocity as follows:

Mass Flow Rate	Velocity
Volume Flow Rate(ṁ) is the amount of mass(m) of a fluid flows through a cross sectional area (A) per unit time (t).	Velocity bar(v) of a fluid is defined as the distance(d) travelled by a fluid within a time period( t).
Mathematically, ṁ= m/t	Mathematically, bar(v)=d/t
Units: kg/s( SI unit), gm/s(CGS unit)	Units: m/s(SI unit), cm/s(CGS unit)

Problems Related to Mass Flow Rate

 Problem 1: A fluid with density 650 kg/m³ is flowing through a duct of inner cross sectional area 25 cm² with a velocity of 30 m/s. Find the mass flow rate of the fluid.

Solution: Here, Density, ρ=650kg/m³

Cross sectional Area, A=25 cm²=0.25m²

Velocity, v=30m/s

The formula for calculating mass flow rate ṁ= ρVA

\dot{m}=  650× 30 × 0.25m = 8400 kg/s

The mass flow rate m  for the above-given data is 4875 kg/s

Problem 2:The mass flow rate of a fluid flowing through a circular pipe is 3600 kg/s, the velocity of the flow is 25 m/s and cross sectional area of the pipe is  10 cm². Calculate the density of the fluid inside the pipe.

Solution:

From the given data,

\dot{m}=  3600 kg/s,

Velocity,v = 25 m/s and

Area of the cross section,A = 10 cm² = 0.10m²

To determine the density of thefluid from the above-given values, we can use the formula,

Density ρ= m/vA

ρ = 3600 / ( 25 * 0.10 ) =  3600 / 2.5

ρ =  1440 kg/m³

The density of the liquid ρ of the fluid passing through the pipe is 1440kg/m³

Frequently Asked Questions(FAQs)

Q1: Write the differences between Mass Flow Rate and Volume Flow Rate.

Answer: The Differences between Mass Flow Rate and Volume Flow Rate are mentioned below:

Mass Flow Rate	Volume Flow Rate
Actual mass of a fluid which travels through a measuring instrument per unit of time	Volume of fluid that passes through a measuring instrument per unit time.
Preferable in case of high accuracy with a high pressure rating	Generally preferred when high accuracy isn’t necessary.
There is no change in mass flow rate with changing pressure and temperature.	Changes in Flow rate occurs with pressure and temperature is changed.
Formula for mass flow rate, ṁ = Density x cross sectional area x velocity	Formula for volume flow rate, Q=Cross sectional area x Av. velocity
Mass flow is measured in kilogram/second	Volume flow rate is measured in litre/second or cubic metre/second.

To know more about Mass Flow Rate(Click here)

In the article we will discuss about the topic of “High Discharge Pressure” and their related facts with types, causes, and how the high discharge pressure is related with the other parameters with several facts.

High discharge pressure can be defined as the pressure of the gas compressor’s which carrying by the suction line into the air conditioning system is facing leakage from the discharge valve is present in the compressor’s output side and combined with an indicator’s lower suction pressure.

The phenomenon named high discharge pressure of an air conditioning system can be easily fixed without facing any problem.

When the dirt is present in the compressor and if it is continuously flow by the coil in the refrigeration system then the flow of the air could not get sufficient place to flow properly in the coils and increases unwanted temperature and pressure. So, if at beginning we focus on cleaning of the dirt then high discharge pressure easily can avoided.

The problem is mainly arising from the compressor. If at the beginning of the process we go through over the compressor then this unwanted high discharge pressure can be easily avoided. If the condition of the air conditioning system is not handling immediately then the compressor it needs to repair.

In the next step we need to observe the condition of the evaporator coil. The refrigerant of the compressor passes through the outlet of the evaporator due to high temperature. In this situation the expansion valve need to open immediately to move the refrigerant.

Or the other process to control the high discharge pressure in the air conditioning system is to observe the expansion valve for the temperature and the pressure.

The phenomenon measured by the measuring instrument which is Bourdon tube pressure gauge, Manometer.

Read more about Gauge pressure: Its important properties with 30 FAQs

What is high discharge pressure?

The main reason behind the high discharge pressure is excess amount of pressurized gas is present in the refrigeration system which is flowing from the compressor’s suction line to evaporator coil.

The high discharge pressure is excess amount of vaporised gas is present in the compressor’s suction line  in the fixed area of the air conditioning system which is increases unwanted temperature and pressure because of the heat transfer is not happed properly.

The main reason behind this situation is the refrigerant present in the compressor of the air conditioning system is not able to transfer into heat which is carrying by the evaporator coil.

The coils are usually made with metal such as copper, tungsten which is used in the high discharge pressure in the air conditioning system. The evaporator coil and condenser unit connected with the help of suction line.

In the suction line present refrigerant is pressurized about 60 – 72 pound per square. When this amount of pressurized refrigerant is crosses the compressor the pressure is arise and thus the inside temperature is also increases. This condition can slow the whole process even can damage the air conditioning system.

Read more about Liquid Refrigerant Coolant : Need to know Facts

High discharge pressure in refrigeration system:

The high discharge pressure is an unwanted situation which is occurs by the present of insufficient compressor of the refrigeration system in the cooling medium which may be water or gas.

The term of insufficient compressor means the leakage should be contained by the discharge valve of the compressor which is situated outside of the compressor. In the refrigeration system the refrigerant is present in the suction line of the compressor which obviously not enough for the cooling medium that could be liquid gas or water.

When the refrigerant of the compressor is not totally transfer into heat then the low head pressure is continuously increases and the pressurized range of the cooling medium became too high near about 72 PSI which is not required to the system. At the high discharge pressure the temperature of the refrigeration system is also became high than the normal temperature because of the present oil could not able to lubricate properly when the cylinders and compressor are too hot.

Read more about Coolant vs Refrigerant : Comparative Analysis and FAQs

High discharge pressure in chillers:

The chillers are works in the basic law of vapour absorption or in the law of vapour absorption.

A device by which heat can be remove with the help of the vapour compressor from a coolant which should be stayed in a liquid form in the refrigeration system is called high discharge pressure in chillers.

If we go through the refrigeration cycle then we could find t first the liquid which is present in refrigeration system is circulated in the heat exchanger for coiling the liquid. The excess amount of heat which is produced in refrigeration system during the refrigeration cycle that would be discharge in the atmosphere to balanced the whole process.

The chillers can be classified in some categories in basic of technology used in the compressor. The classification chillers name given in below,

Reciprocating chillers

Centrifugal chillers

Scroll chillers

Screw chillers

The chillers classified in the basis of system names are given below

Water chillers

Air chillers

Evaporative condensed chillers

High discharge pressure cause:

The reason of high discharge pressure is briefly summarize in below,

1. When the compressor of the air conditioning system carry the cooling medium.

The cooling medium can be water or liquid gas.

2. Temperature of the cooling medium is more than the normal temperature for the refrigeration cycle in air conditioning system.

3. Size of the evaporator is too high: If the size of the evaporator is excess than the normal size then the unbalanced situation is occurred.

4. Get not enough space to floe the refrigerant in the air conditioning system.

5. Leakage from the valve of the compressor:

In the air conditioning system one of the common problems for the phenomenon of high discharge pressure is the leakage from the compressor valve of the compressor. This is very difficult to detect but when this condition occur the gasses are emitted from the holes and the air flow is not flow properly .Thus discharge gas is moves into the compressor cylinder by the down stroke of the crankshaft.

When the sealing of the discharge valve is not done properly thus the causes low head pressure and increases the temperature .The discharge temperature became more than the usual temperature of the refrigeration cycle.

 Sometimes the gases which are discharge from the compressor cylinder is run through short cycle, in this situation the flow of the present refrigerants became low. As a result the pressure and temperature became less for the heat load which is present in the condenser.

When the low refrigerant go through the condenser, the rate of the heat is reduced, means the sub cooling of condenser causes high suction pressure.

6. Damage of the piston ring of the compressor:

When the emit gasses facing leakage due to the piston ring of the compressor the pressure is developed than the normal pressure and the high suction pressure is happened. During the compressor stroke the piston ring of the compressor is produce low head pressure.

Read more about Liquid Refrigerant in Compressor: Need to Know Critical Facts

7. Leakage of the return line of the oil separator:

The purpose of the oil separator is to differentiate and control the level of the high and low sides of the air conditioning system. In the refrigeration system the oil separator is place in the higher side of the level and the compressor crankcase is situated in the lower side of the air condition system. The oil is flow by high level means the oil separator to low side of the level means in the crankcase.

If the oil is could not flow properly in the air conditioning system then high pressure is occur and high suction pressure is appear.

8. When the refrigerant is overcharged:

If the size of the electronic expansion valve is large than the usual size then the evaporator is overfeed and causes the high suction pressure.

9. Excessive temperature:

When the flow of discharge gasses is not go properly through the suction line the temperature increases and high suction pressure is appear.

High discharge pressure type:

High discharge pressure is the inside condition of the air conditioning system. When some unnecessary situation or object is present in the refrigeration system the temperature is increases and causes a lot of problem.

The high discharge pressure is a phenomenon in the air conditioning system which is appears in present of insufficient compressor. So, the classification of high discharge pressure cannot be done only the reading of the air-conditioning system can be done.

The air conditioning system works in the between the range of 155 PSI to 30 PSI.

The reading ranges of the air conditioning system is given below,

1.100 PSI / 100 PSI – In this range reading we could understand that the generated power of the refrigeration system is can not reach to the compressor thus the compressor of the air conditioning system is not properly engaged.

2.50 PSI / 50 PSI – In this reading of the range the clutch of the refrigeration system is not engaged.

3.150 PSI / 30 PSI – If the water is present in the refrigeration cycle as the cooling medium then the range is belong to the refrigeration system.

4.150 PSI / > 10 PSI – The range of the conditioning system can help to recognize us that, there should some leakage definitely present in the refrigeration system. If at this situation the technician tried to find the leakage then the condition of the refrigeration system could not go so bad but the detection of the leakage is not too easy work.

5.125 PSI / 30 PSI – The range tells us that the refrigeration system may be oil is present in the compressor of the return line from the oil separator. The alternative reason behind the range can be the charge of the refrigeration system is not enough.

6.160 PSI / 10 PSI  

7. 200 PSI / 70 PSI

8. 250 PSI / 30 PSI

9. 250 PSI / 50 PSI

10. 225 PSI / 80 PSI