HYDRAULICS (Calculations used in fireground operations) ... programme, on the
subject of Hydraulics, as relevant to Rescue and Fire Fighting Services.
Issue 2 Mar 05
INTERNATIONAL FIRE TRAINING CENTRE
FIREFIGHTER INITIAL HYDRAULICS (Calculations used in fireground operations) Throughout this not he means he/she and his means his/hers. Areas considered to be of prime importance are in bold type.
INTRODUCTION This training note is intended to provide information to students attending Firefighter Initial programme, on the subject of Hydraulics, as relevant to Rescue and Fire Fighting Services (RFFS) employed at airports. This training note should be read in conjunction with the previously issued Hydraulics Training Note, which deals with the basic concepts of Hydraulics. AIM To ensure that all students attending Firefighter Initial programmes understand the principles of Hydraulics and fully appreciate the role of Hydraulics in the calculations used for fireground operations. OBJECTIVES At the end of the instructional session dealing with this subject and after detailed study of this note, you will be able to •
State the formulas commonly used
•
Apply formulas commonly used to a range of theoretical situation
CONTENTS The subject will be dealt with under the following headings: • • • • • • •
General Review Head and Pressure Formulas Rectangular Tanks Circular Tanks Nozzle discharge Summary
GENERAL REVIEW General A basic knowledge is important for the safe and efficient movement of water for firefighting purposes. This note is produced to introduce you to hydraulics (movement of water) and to assist you throughout your career. It should be retained for future reference. This note is provided as an addition to the Basic Concepts of Hydraulics, as the next stage is to appreciate and understand the need for fireground calculations. Head To the Fire Service this means the vertical height of the surface of the water above the point where the pressure is to be measured. This is measured in metres (m) and expressed as a metrehead. 1 cubic metre is expressed as 1m3. Therefore if 1m3 of water has a mass of 1000 kgs (capacity of 1000 litres) it then exerts a force at its base of 1000 x 9.81 N/m2 that = 9810 N/m2. Remember 9.81N is the force due to gravity created by 1 kg of water at its base. So from the information given above we can say pressure equals 9810 x Head (in metres) Newton per square metre. P = 9810 x H
Answer would be in N/m2.
So if we knew the pressure and wanted to know the head we could say H = Pressure 9810
Answer would be in metres.
However the N/m2 is a small unit of measurement and involves us in using large numbers. We can simplify. Atmospheric pressure = 101325 N/m2. 1 Bar = 100000 N/m2. So we use the Bar instead for fireground calculations and this will give us an approximate error of 2%. Remember 9810 N/m2 exerted by 1m3 of water. Round this off to 10000 N/m2. 2
Remember 100000 N/m – 1 Bar. Therefore if we set it out like this 1000 cancel down = 1 or 0.1 Bar 10000 10 So for every metre rise in the level of water will equal 1/10 or 0.1 Bar rise on a pressure gauge. Then our calculation to find pressure and head becomes Pressure = Head in metres) 10 Answers in Bars Head = 10 x Pressure (in Bar) Answer in metres An example of this – If we had a column of water 50m high, what is the pressure of its base, (a) and what is the pressure half way up (b)? a
P = (H)50 Answer 5 Bars. 10
Issue 2 Mar 05
b
P = (H)25 Answer 2.5 Bar 10
A gauge registering 7 Bars, what is the head of water? H = 10 x 7 Bars. Answer 70 meters high. A gauge registering 2.5 Bars, what is the head? H = 10 x 2.5 Answer 25m. So 10m head = 1 Bar FORMULAS The calculation of the volume of water in any tank is done in two stages: • calculate the volume in cubic metres • convert the volume in cubic metres to a volume in litres Remember there are 1000 litres in 1 cubic metre. Rectangular Tanks Volume of tank = length x breadth x height measured in metres Answer in cubic metres l x b x h = m3 Multiply by 1000 Answer is in litres If you are asked for the contents of the tank you would have used the actual depth of water in the tank instead of the depth of the tank. Circular Tanks The first step is to see how to calculate the cross sectional area of a circular tank. The area of a circle (or cross sectional area of a circular tank) - π x radius x radius. Put this into symbols – Area of circle - πr2
π = 22 7
Example – What is the area of a circle whose radius is 5 metres? Area of circle=
πr2
=
22 x 5 x 5 7
=
110 x 5 7
=
550 7
=
78.571
=
78.57 to two places of decimals
Area of circle equals 78.57 square metres. Suppose the above was the radius of a tank 10 metres deep and we required to know the volume of the tank.
Issue 2 Mar 05
Volume
= cross sectional area x depth = 78.57 x 10 = 785.7 cubic metres
Contents in litres 1000 litres in 1 cubic metre Contents
= 785.7 x 1000
Contents
= 785700 litres
Capacity of hose When calculating the capacity of hose it is usual to calculate the capacity of one metre length. Capacity of hose = 8d2 litres per metre 10000 d
= 70 millimetre
Therefore capacity
= 8 x 70 x 70 10000 = 8 x 49 1000 = 392 1000
Therefore
Capacity
= 3.92 litre
Use this formula to calculate the capacity of 300 metres of 90 millimetre hose Capacity
d Capacity
= 8d2 litres per metre 10000 = 90 millimetre = 8 x 90 x 90 10000
x 300
= 72 x 9 x 3 = 648 x 3 = 1944 litre Nozzle Discharge The function of a nozzle at the end of a hose line is to convert pressure energy into velocity or kinetic energy. This is done by reducing the area of the cross-section through which the water must pass. The velocity of the water issuing from the nozzle varies inversely with the size of the nozzle. That is to say for the same rate of flow, if we reduce the size of the nozzle, the velocity is increased or if we increase the nozzle size then the velocity is reduced.
Issue 2 Mar 05
NOTE Doubling the size of the nozzle does not allow double the quantity. It allows four times the quantity to pass through if the same pressure is maintained. Remember Law No 3 in frictional loss. Calculating Nozzle Discharge It is useful for firefighters to know the discharge of a nozzle particularly at protracted pumping incidents. The formula for nozzle discharge is: L = 2/3 d2 √P In this formula, what do the symbols L, P, d2 √P stand for? L
= discharge in litres per minute
d
= diameter of nozzle in millimetres
P
= pressure at the nozzle in bars
√
= square root, therefore √P is the square root of the pressure
Example
What is the discharge of a 20 mm nozzle operating at a branch pressure of 4 bars. formula
= L = 2/3 d2 √P = 2/3 x 20 x 20 x √4 = 2/3 x 20 x 20 x2 = 1600 3 533 litres per minute
SUMMARY As firefighters we need to appreciate and fully understand where and how calculations fit into our role. Therefore we need to recognise and be able to interpret this in a way that ensures safe but effective firefighting conditions apply.
