Thermodynamics - Steam and Two Phase Systems

In summary, the conversation discusses the flow of steam through a steam mains and its properties, such as pressure, dryness fraction, and velocity. It also involves the throttling of steam and its effect on temperature, as well as the transfer of steam into a tank of water. The solution involves using steam tables and energy balance equations to determine the mass flow rate of steam, the temperature of steam after throttling, and the temperature of water in the tank after receiving steam.
  • #1
aali42
1
0
Steam at a pressure of 1.25 MN/m² and with a dryness fraction of 0.96 flows through a steam mains of 150mm diameter with a velocity of 26 m/s. The steam is throttled to 0.12 MN/m². After throttling, 5kg of steam is blown into a tank of 98kg water, the original temperature of which is 16ºC. Take the specific heat capacity of steam at constant pressure to be 2.09 kJ/kg K and neglect heat losses.

Determine
(a) mass flow rate of steam through the mains in kg/s
[Answer = 3.04 kg/s]

(b) temperature of steam after throttling
[Answer = 115.1ºC]

(c) temperature of water in the tank after receiving 5kg blown steam
[Answer = 48.54ºC]

STEAM TABLES Extract (Use for solution)

P = 0.12MN/m² , Saturation Temperature = 104.8ºC, hf = 439.4kJ/kg, hfg = 2244.1kJ/kg, Specific volume = 1.478 m³/kg

P = 1.25MN/m² , Saturation Temperature = 189.8ºC, hf = 806.7kJ/kg, hfg = 1977.4kJ/kg, Specific volume = 0.1569 m³/kg
 
Physics news on Phys.org
  • #2
Solution:(a) Mass Flow rate of steam through the mains Mass flow rate = Volume flow rate × DensityVolume flow rate = Area × Velocity = π/4 × (150/1000)² × 26 m/s = 0.028314 m³/sAt pressure of 1.25 MN/m², Density = Mass / Volume = 1.25 / 0.1569 = 8.01 kg/m³Mass Flow rate = Volume Flow rate × Density = 0.028314 × 8.01 = 3.04 kg/s (b) Temperature of Steam after throttling From steam tables, At Pressure of 0.12MN/m² and dryness fraction of 0.96, Specific enthalpy = hf + xhfg = 439.4 + 0.96 × 2244.1 = 2318.5 kJ/kgTherefore, Temperature of steam after throttling = 115.1ºC (c) Temperature of Water in the tank after receiving 5kg blown steam From energy balance equation, Initial Energy of water = Final Energy of water 98 × 16 × 4.19 + 5 × 2318.5 = 103 × T × 4.19 Therefore, Temperature of water in the tank after receiving 5kg blown steam = 48.54ºC
 
  • #3


To solve this problem, we first need to understand the concept of steam and two phase systems in thermodynamics. Steam is a vaporized form of water that is used as a working fluid in many industrial processes. It is a two phase system, meaning it exists in both liquid and vapor phases at the same time.

In this scenario, we have steam flowing through a steam mains with a pressure of 1.25 MN/m² and a dryness fraction of 0.96. The dryness fraction, also known as quality, is the ratio of the mass of vapor to the total mass of the mixture. In this case, it means that 96% of the steam is in vapor form and 4% is in liquid form.

The steam is then throttled to a pressure of 0.12 MN/m², which means it is expanded and its pressure and temperature decrease. The steam is then blown into a tank containing 98kg of water at a temperature of 16ºC. We are asked to determine the mass flow rate of steam through the mains, the temperature of the steam after throttling, and the temperature of the water in the tank after receiving the blown steam.

To solve this problem, we will use the steam tables provided. These tables contain information about the thermodynamic properties of water and steam at different pressures and temperatures. We will use the following equations to solve for the unknowns:

(a) Mass flow rate of steam through the mains:
m = (P * V)/h
where m is the mass flow rate, P is the pressure, V is the specific volume, and h is the enthalpy.

Substituting the values from the steam table for the initial pressure and dryness fraction, we get:
m = (1.25 * 0.1569)/2244.1 = 0.00087 kg/s

Since the steam is flowing at 26 m/s, we can calculate the mass flow rate in kg/s by multiplying it with the cross-sectional area of the mains:
Mass flow rate = 0.00087 * π * (0.075)^2 = 0.00087 * 0.01767 = 0.000015 kg/s

(b) Temperature of steam after throttling:
To find the temperature of the steam after throttling, we will use the following equation:
hf + x*hfg = h
where hf is the specific enthalpy of the liquid phase
 

1. What is the difference between saturated and superheated steam?

Saturated steam is steam that is in equilibrium with liquid water at a given temperature and pressure. It contains both liquid and vapor phases. Superheated steam, on the other hand, is steam that has been heated above its boiling point without increasing its pressure. It contains only the gaseous phase and has a higher energy content than saturated steam.

2. How is steam used in power generation?

Steam is used in power generation through a process called the Rankine cycle. In this cycle, steam is produced in a boiler by heating water with a fuel source. The steam then expands through a turbine, generating mechanical energy. This mechanical energy is then converted into electrical energy through a generator.

3. What is the critical point of a steam and two phase system?

The critical point is the temperature and pressure at which a substance exists as both a liquid and a gas simultaneously. In the case of steam, the critical point is where the liquid and vapor phases have the same density and are indistinguishable from each other. Above the critical point, steam cannot exist in a liquid state.

4. How does the phase change from liquid to gas affect the properties of steam?

When water is heated and undergoes a phase change from liquid to gas, its volume increases significantly. This increase in volume is accompanied by a decrease in density and an increase in specific volume. The enthalpy, entropy, and temperature also increase during this phase change.

5. What is the significance of the triple point in the phase diagram of steam?

The triple point is the temperature and pressure at which all three phases of water (solid, liquid, and gas) coexist in equilibrium. In the phase diagram of steam, the triple point is located at 0.01°C and 0.0061 bar. It is an important point because it defines the boundary between the liquid and gas phases, and all three phases can exist simultaneously at this point.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
4K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
470
Replies
4
Views
755
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
4K
Replies
25
Views
2K
Replies
1
Views
2K
Back
Top