What is Pressure
Pressure is a measure of the force exerted per unit area on the boundaries of a substance. The standard unit for pressure in the SI system is the Newton per square meter or pascal (Pa). Mathematically:
p = F/A
where
 p is the pressure
 F is the normal force
 A is the area of the boundary
Pascal is defined as force of 1N that is exerted on unit area.
 1 Pascal = 1 N/m^{2}
However, for most engineering problems it is fairly small unit, so it is convenient to work with multiples of the pascal: the kPa, the bar, and the MPa.
 1 MPa 10^{6} N/m^{2}
 1 bar 10^{5} N/m^{2}
 1 kPa 10^{3} N/m^{2}
In general, pressure or the force exerted per unit area on the boundaries of a substance is caused by the collisions of the molecules of the substance with the boundaries of the system. As molecules hit the walls, they exert forces that try to push the walls outward. The forces resulting from all of these collisions cause the pressure exerted by a system on its surroundings. Pressure as an intensive variable is constant in a closed system. It really is only relevant in liquid or gaseous systems.
Static pressure is one of the terms of Bernoulli’s equation:
The Bernoulli’s effect causes the lowering of fluid pressure (static pressure – p) in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy (dynamic pressure – ½.ρ.v^{2}) must increase at the expense of pressure energy (static pressure – p).
The simplified form of Bernoulli’s equation can be summarized in the following memorable word equation:
static pressure + dynamic pressure = total pressure (stagnation pressure)
Total and dynamic pressure are not pressures in the usual sense – they cannot be measured using an aneroid, Bourdon tube or mercury column.
This effect causes the lowering of fluid pressure (static pressure) in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy (dynamic pressure – ½.ρ.v^{2}) must increase at the expense of pressure energy (static pressure – p).
As can be seen, dynamic pressure is dynamic pressure is one of the terms of Bernoulli’s equation. In incompressible fluid dynamics, dynamic pressure is the quantity defined by:
The simplified form of Bernoulli’s equation can be summarized in the following memorable word equation:
static pressure + dynamic pressure = total pressure (stagnation pressure)
Total and dynamic pressure are not pressures in the usual sense – they cannot be measured using an aneroid, Bourdon tube or mercury column.
To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use the term static pressure to distinguish it from total pressure and dynamic pressure. The term static pressure is identical to the term pressure, and can be identified for every point in a fluid flow field. Dynamic pressure is the difference between stagnation pressure and static pressure.
Stagnation pressure is equal to the sum of the freestream dynamic pressure and freestream static pressure.
Static pressure and dynamic pressure are terms of Bernoulli’s equation:
The Bernoulli’s effect causes the lowering of fluid pressure (static pressure – p) in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy (dynamic pressure – ½.ρ.v^{2}) must increase at the expense of pressure energy (static pressure – p).
The simplified form of Bernoulli’s equation can be summarized in the following memorable word equation:
static pressure + dynamic pressure = total pressure (stagnation pressure)
Total and dynamic pressure are not pressures in the usual sense – they cannot be measured using an aneroid, Bourdon tube or mercury column.
Stagnation pressure is sometimes referred to as pitot pressure because it is measured using a pitot tube. A Pitot tube is a pressure measurement instrument used to measure fluid flow velocity. Velocity can be determined using the following formula:
where:
 u is flow velocity to be measured in m/s,
 p_{s }is stagnation or total pressure in Pa,
 p_{t} is static pressure in Pa,
 ρ is fluid density in kg/m^{3}.
Pressure Scales – Pressure Units
Pascal – Unit of Pressure
As was discussed, the SI unit of pressure and stress is the pascal.
 1 pascal 1 N/m^{2} = 1 kg / (m.s^{2})
Pascal is defined as one newton per square metre. However, for most engineering problems it is fairly small unit, so it is convenient to work with multiples of the pascal: the kPa, the bar, and the MPa.
 1 MPa 10^{6} N/m^{2}
 1 bar 10^{5} N/m^{2}
 1 kPa 10^{3} N/m^{2}
The unit of measurement called standard atmosphere (atm) is defined as:
 1 atm = 101.33 kPa
The standard atmosphere approximates to the average pressure at sealevel at the latitude 45° N. Note that, there is a difference between the standard atmosphere (atm) and the technical atmosphere (at).
A technical atmosphere is a nonSI unit of pressure equal to one kilogramforce per square centimeter.
 1 at = 98.67 kPa
Pounds per square inch – psi
The standard unit in the English system is the poundforce per square inch (psi). It is the pressure resulting from a force of one poundforce applied to an area of one square inch.
 1 psi 1 lbf/in^{2} = 4.45 N / (0.0254 m)^{2} ≈ 6895 kg/m^{2}
Therefore, one pound per square inch is approximately 6895 Pa.
The unit of measurement called standard atmosphere (atm) is defined as:
 1 atm = 14.7 psi
The standard atmosphere approximates to the average pressure at sealevel at the latitude 45° N. Note that, there is a difference between the standard atmosphere (atm) and the technical atmosphere (at).
A technical atmosphere is a nonSI unit of pressure equal to one kilogramforce per square centimeter.
 1 at = 14.2 psi
Bar – Unit of Pressure
The bar is a metric unit of pressure. It is not part of the International System of Units (SI). The bar is commonly used in the industry and in the meteorology, and an instrument used in meteorology to measure atmospheric pressure is called barometer.
One bar is exactly equal to 100 000 Pa, and is slightly less than the average atmospheric pressure on Earth at sea level (1 bar = 0.9869 atm). Atmospheric pressure is often given in millibars where standard sea level pressure is defined as 1013 mbar, 1.013 bar, or 101.3 (kPa).
Sometimes, “Bar(a)” and “bara” are used to indicate absolute pressures and “bar(g)” and “barg” for gauge pressures.
Absolute vs. Gauge Pressure
Pressure as discussed above is called absolute pressure. Often it will be important to distinguish between absolute pressure and gauge pressure. In this article the term pressure refers to absolute pressure unless explicitly stated otherwise. But in engineering we often deal with pressures, that are measured by some devices. Although absolute pressures must be used in thermodynamic relations, pressuremeasuring devices often indicate the difference between the absolute pressure in a system and the absolute pressure of the atmosphere existing outside the measuring device. They measure the gauge pressure.
 Absolute Pressure. When pressure is measured relative to a perfect vacuum, it is called absolute pressure (psia). Pounds per square inch absolute (psia) is used to make it clear that the pressure is relative to a vacuum rather than the ambient atmospheric pressure. Since atmospheric pressure at sea level is around 101.3 kPa (14.7 psi), this will be added to any pressure reading made in air at sea level.
 Gauge Pressure. When pressure is measured relative to atmospheric pressure (14.7 psi), it is called gauge pressure (psig). The term gauge pressure is applied when the pressure in the system is greater than the local atmospheric pressure, p_{atm}. The latter pressure scale was developed because almost all pressure gauges register zero when open to the atmosphere. Gauge pressures are positive if they are above atmospheric pressure and negative if they are below atmospheric pressure.
p_{gauge} = p_{absolute} – p_{absolute; atm}
 Atmospheric Pressure. Atmospheric pressure is the pressure in the surrounding air at – or “close” to – the surface of the earth. The atmospheric pressure varies with temperature and altitude above sea level. The Standard Atmospheric Pressure approximates to the average pressure at sealevel at the latitude 45° N. The Standard Atmospheric Pressure is defined at sealevel at 273^{o}K (0^{o}C) and is:
 101325 Pa
 1.01325 bar
 14.696 psi
 760 mmHg
 760 torr
 Negative Gauge Pressure – Vacuum Pressure. When the local atmospheric pressure is greater than the pressure in the system, the term vacuum pressure is used. A perfect vacuum would correspond to absolute zero pressure. It is certainly possible to have a negative gauge pressure, but not possible to have a negative absolute pressure. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of −21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa).
p_{vacuum} = p_{absolute; atm} – p_{absolute}
For example, a car tire pumped up to 2.5 atm (36.75 psig) above local atmospheric pressure (let say 1 atm or 14.7 psia locally), will have an absolute pressure of 2.5 + 1 = 3.5 atm (36.75 + 14.7 = 51.45 psia or 36.75 psig).
On the other hand condensing steam turbines (at nuclear power plants) exhaust steam at a pressure well below atmospheric (e.g. at 0.08 bar or 8 kPa or 1.16 psia) and in a partially condensed state. In relative units it is a negative gauge pressure of about – 0.92 bar, – 92 kPa, or – 13.54 psig.
Ideal Gas Law
Any equation that relates the pressure, temperature, and specific volume of a substance is called an equation of state. The simplest and bestknown equation of state for substances in the gas phase is the Ideal Gas equation of state. It was first stated by Émile Clapeyron in 1834 as a combination of the empirical Boyle’s law, Charles’ law and Avogadro’s Law. This equation predicts the pvT behavior of a gas quite accurately for dilute or lowpressure gases. In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume.
pV = nRT
where:
 p is the absolute pressure of the gas
 n is the amount of substance
 T is the absolute temperature
 V is the volume
 R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,
In this equation the symbol R is a constant called the universal gas constant that has the same value for all gases—namely, R = 8.31 J/mol K.
The power of the ideal gas law is in its simplicity. When any two of the thermodynamic variables, p, v, and T are given, the third can easily be found. An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. An ideal gas can be visualized as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In reality, no real gases are like an ideal gas and therefore no real gases follow the ideal gas law or equation completely. At temperatures near a gases boiling point, increases in pressure will cause condensation to take place and drastic decreases in volume. At very high pressures, the intermolecular forces of a gas are significant. However, most gases are in approximate agreement at pressures and temperatures above their boiling point. The ideal gas law is utilized by engineers working with gases because it is simple to use and approximates real gas behavior.
Typical Pressures in Engineering – Examples
The pascal (Pa) as a unit of pressure measurement is widely used throughout the world and has largely replaced the pounds per square inch (psi) unit, except in some countries that still use the Imperial measurement system, including the United States. For most engineering problems pascal (Pa) is fairly small unit, so it is convenient to work with multiples of the pascal: the kPa, the MPa, or the bar. Following list summarizes a few examples:
 Typically most of nuclear power plants operates multistage condensing steam turbines. These turbines exhaust steam at a pressure well below atmospheric (e.g. at 0.08 bar or 8 kPa or 1.16 psia) and in a partially condensed state. In relative units it is a negative gauge pressure of about – 0.92 bar, – 92 kPa, or – 13.54 psig.
 The Standard Atmospheric Pressure approximates to the average pressure at sealevel at the latitude 45° N. The Standard Atmospheric Pressure is defined at sealevel at 273^{o}K (0^{o}C) and is:
 101325 Pa
 1.01325 bar
 14.696 psi
 760 mmHg
 760 torr
 Car tire overpressure is about 2.5 bar, 0.25 MPa, or 36 psig.
 Steam locomotive fire tube boiler: 150–250 psig
 A highpressure stage of condensing steam turbine at nuclear power plant operates at steady state with inlet conditions of 6 MPa (60 bar, or 870 psig), t = 275.6°C, x = 1
 A boiling water reactor is cooled and moderated by water like a PWR, but at a lower pressure (e.g. 7MPa, 70 bar, or 1015 psig), which allows the water to boil inside the pressure vessel producing the steam that runs the turbines.
 Pressurized water reactors are cooled and moderated by highpressure liquid water (e.g. 16MPa, 160 bar, or 2320 psig). At this pressure water boils at approximately 350°C (662°F), which provides subcooling margin of about 25°C.
 The supercritical water reactor (SCWR) is operated at supercritical pressure. The term supercritical in this context refers to the thermodynamic critical point of water (T_{CR} = 374 °C; p_{CR} = 22.1 MPa)
 Common rail direct fuel injection: On diesel engines, it features a highpressure (over 1 000 bar or 100 MPa or 14500 psi) fuel rail.
Pressurized water reactors use a reactor pressure vessel (RPV) to contain the nuclear fuel, moderator, control rods and coolant. They are cooled and moderated by highpressure liquid water (e.g. 16MPa). At this pressure water boils at approximately 350°C (662°F). This high pressure is maintained by pressurizer. Inlet temperature of the water is about 290°C (554°F). The water (coolant) is heated in the reactor core to approximately 325°C (617°F) as the water flows through the core. As it can be seen, the reactor has approximately 25°C subcooled coolant (distance from the saturation).
A pressurizer is a component of a pressurized water reactor. Pressure in the primary circuit of PWRs is maintained by a pressurizer, a separate vessel that is connected to the primary circuit (hot leg) and partially filled with water which is heated to the saturation temperature (boiling point) for the desired pressure by submerged electrical heaters.
On the other hand there are spray lines to decrease pressure inside the pressurizer, which in turn causes decrease in pressure in reactor coolant system. These spray lines sprays reactor coolant from the cold leg of a loop into the steam space and condenses a portion of the steam. The quenching action reduces pressure and limits the pressure increases.
Typically most of nuclear power plants operates multistage condensing steam turbines. In these turbines the highpressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure; 6 MPa; 275.6°C) from a steam generator and exhaust it to moisture separatorreheater (point D). The steam must be reheated in order to avoid damages that could be caused to blades of steam turbine by low quality steam. The reheater heats the steam (point D) and then the steam is directed to the lowpressure stage of steam turbine, where expands (point E to F). The exhausted steam is at a pressure well below atmospheric (absolute pressure of 0.008 MPa), and is in a partially condensed state (point F), typically of a quality near 90%.
See also: Wet Steam
See also: Steam Tables
α_{P} = ^{dρ}⁄_{dP}
It is expressed in units of pcm/MPa. The magnitude and sign (+ or ) of the pressure coefficient is primarily a function of the moderatortofuel ratio. That means it primarily depends on certain reactor design.
Although water is considered to be incompressible, in reality, it is slightly compressible (especially at 325°C (617°F)). It is obvious, the effect of pressure in the primary circuit have similar consequences as the moderator temperature. In comparison with effects of moderator temperature changes, changes in pressure have of lower order impact on reactivity and the causes are only in the density of moderator, not in the change of microscopic crosssections.
Pressure Loss – Fluids
Summary of: Head Loss – Pressure Loss
 Head loss or pressure loss are the reduction in the total head (sum of potential head, velocity head, and pressure head) of a fluid caused by the friction present in the fluid’s motion.
 Head loss and pressure loss represent the same phenomenon – frictional losses in pipe and losses in hydraulic components, but they are expressed in different units.
 Head loss of hydraulic system is divided into two main categories:
 Major Head Loss – due to friction in straight pipes
 Minor Head Loss – due to components as valves, bends…

Darcy’s equation can be used to calculate major losses.
 A special form of Darcy’s equation can be used to calculate minor losses.
 The friction factor for fluid flow can be determined using a Moody chart.
 The friction factor for laminar flow is independent of roughness of the pipe’s inner surface. f = 64/Re
 The friction factor for turbulent flow depends strongly on the relative roughness. It is determined by the Colebrook equation. It must be noted, at very large Reynolds numbers, the friction factor is independent of the Reynolds number.
 The minor losses are roughly proportional to the square of the flow rate and therefore they can be easy integrated into the DarcyWeisbach equation through resistance coefficient K.
 As a local pressure loss fluid acceleration in a heated channel can be also considered.
Critical Pressure of Water
At pressure, that is higher than the critical pressure, water is in special state, that is known as supercritical fluid state. A supercritical fluid is a fluid that is at pressures higher than its thermodynamic critical values. At the critical and supercritical pressures a fluid is considered as a singlephase substance in spite of the fact that all thermophysical properties undergo significant changes within the critical and pseudocritical regions.
For water, the critical parameters are the following:
 P_{cr} = 22.09 MPa
 T_{cr} = 374.14 °C (or 647.3 K)
 v_{cr} = 0.003155 m3/kg
 u_{f} = u_{g} = 2014 kJ/kg
 h_{f} = h_{g }= 2084 kJ/kg
 s_{f} = s_{g} =4.406 kJ/kg K
See also: Critical Point of Water
See also: Supercritical Fluid
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