Density of Water – Specific Volume of Water

Density of Water – H2O

properties of waterPure water has its highest density 1000 kg/m3 at temperature 3.98oC (39.2oF). Water differs from most liquids in that it becomes less dense as it freezes. It has a maximum of density at 3.98 °C (1000 kg/m3), whereas the density of ice is 917 kg/m3. It differs by about 9% and therefore ice floats on liquid water. It must be noted, the change in density is not linear with temperature, because the volumetric thermal expansion coefficient for water is not constant over the temperature range. The density of water (1 gram per cubic centimetre) was originally used to define the gram. The density (⍴) of a substance is the reciprocal of its specific volume (ν).

ρ = m/V = 1/ν

The specific volume (ν) of a substance is the total volume (V) of that substance divided by the total mass (m) of that substance (volume per unit mass). It has units of cubic meter per kilogram (m3/kg).

Density of Water - Specific Volume

 
Changes of Density
In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure always increases the density of a material. The effect of pressure on the densities of liquids and solids is very very small. On the other hand, the density of gases is strongly affected by pressure. This is expressed by compressibility. Compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change.

The effect of temperature on the densities of liquids and solids is also very important. Most substances expand when heated and contract when cooled. However, the amount of expansion or contraction varies, depending on the material. This phenomenon is known as thermal expansion. The change in volume of a material which undergoes a temperature change is given by following relation:

thermal-expansion

where ∆T is the change in temperature, V is the original volume, ∆V is the change in volume, and αV is the coefficient of volume expansion.

It must be noted, there are exceptions from this rule. For example, water differs from most liquids in that it becomes less dense as it freezes. It has a maximum of density at 3.98 °C (1000 kg/m3), whereas the density of ice is 917 kg/m3. It differs by about 9% and therefore ice floats on liquid water

Coolant acceleration in a reactor core
See also: Fluid Acceleration – Pressure Loss

It is an illustrative example, following data do not correspond to any reactor design.

Continuity Equation - Flow Rates through Reactor
Example of flow rates in a reactor. It is an illustrative example, data do not represent any reactor design.

Pressurized water reactors are cooled and moderated by high-pressure liquid water (e.g. 16MPa). At this pressure water boils at approximately 350°C (662°F).  Inlet temperature of the water is about 290°C (⍴ ~ 720 kg/m3). The water (coolant) is heated in the reactor core to approximately 325°C (⍴ ~ 654 kg/m3) as the water flows through the core.

The primary circuit of typical PWRs is divided into 4 independent loops (piping diameter ~ 700mm), each loop comprises a steam generator and one main coolant pump. Inside the reactor pressure vessel (RPV), the coolant first flows down outside the reactor core (through the downcomer). From the bottom of the pressure vessel, the flow is reversed up through the core, where the coolant temperature increases as it passes through the fuel rods and the assemblies formed by them.

Calculate:

  • Pressure loss due to the coolant acceleration in an isolated fuel channel

 when

  • channel inlet flow velocity is equal to  5.17 m/s
  • channel outlet flow velocity is equal to  5.69 m/s

Solution:

The pressure loss due to the coolant acceleration in an isolated fuel channel is then:

coolant acceleration - example

This fact has important consequences. Due to the different relative power of fuel assemblies in a core, these fuel assemblies have different hydraulic resistance and this may induce local lateral flow of primary coolant and it must be considered in thermal-hydraulic calculations.

See also: How density influences reactor reactivity

Density of Steam

dry-steam-saturated-vapor-minWater and steam are a common medium because their properties are very well known. Their properties are tabulated in so called Steam Tables. In these tables the basic and key properties, such as pressure, temperature, enthalpy, density and specific heat, are tabulated along the vapor-liquid saturation curve as a function of both temperature and pressure.

The density (⍴) of any substance is the reciprocal of its specific volume (ν).

ρ = m/V = 1/ν

The specific volume (ν) of a substance is the total volume (V) of that substance divided by the total mass (m) of that substance (volume per unit mass). It has units of cubic meter per kilogram (m3/kg).

See also: Supercritical Fluid

steam properties - steam tables

Density of Heavy Water

Pure heavy water (D2O) has a density about 11% greater than water, but is otherwise physically and chemically similar.

This difference is caused by the fact, the deuterium nucleus is twice as heavy as hydrogen nucleus. Since about 89% of the molecular weight of water comes from the single oxygen atom rather than the two hydrogen atoms, the weight of a heavy water molecule, is not substantially different from that of a normal water molecule. The molar mass of water is M(H2O) = 18.02 and the molar mass of heavy water is M(D2O) = 20.03 (each deuterium nucleus contains one neutron in contrast to hydrogen nucleus), therefore heavy water (D2O) has a density about 11% greater (20.03/18.03 = 1.112).

Pure heavy water (D2O) has its highest density 1110 kg/m3 at temperature 3.98oC (39.2oF). Also heavy water differs from most liquids in that it becomes less dense as it freezes. It has a maximum of density at 3.98 °C (1110 kg/m3), whereas the density of its solid form ice is 1017 kg/m3. It must be noted, the change in density is not linear with temperature, because the volumetric thermal expansion coefficient for water is not constant over the temperature range.

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See above:

Thermodynamic Properties