Thermo conservtion of mass

In summary: Therefore, the inlet velocity is:V1 = 20.3538 kg/s/(0.502 kg/m3 * 0.013352 m2) = 299.87 m/sAnd the inlet volume flow rate is:m1 = ρ1 * A1 * V1 = (0.502 kg/m3 * 0.013352 m2 * 299.87 m/s) = 20.3537 kg/sIn summary, we can use the continuity equation and the ideal gas law to solve for the inlet velocity and volume flow rate of water entering a boiler at 7 Mpa and 65oC
  • #1
MEAHH
10
0

Homework Statement


Water enters the constant 130-mm inside diameter tubes of a boiler at 7 Mpa and 65oC and leaves the tubes at 6 Mpa and 4500C with a velocity of 80 m/s. Calculate the velocity at the inlet and the inlet volume flow rate

Homework Equations





The Attempt at a Solution


so i thought i could find mass flow rate at state 2, then use this to fine velocity at state 1 but i cannot find the specific volume at state 1

mass flow rate=(1/v2) A V2=20.3538kg/s
massflowrate=(1/v1)A V1
 
Physics news on Phys.org
  • #2


your response would be:

Hello,

Thank you for sharing this problem with the forum. Based on the given information, we can use the continuity equation to solve for the inlet velocity and volume flow rate. The continuity equation states that the mass flow rate at any point in a system is equal to the product of the density, velocity, and cross-sectional area at that point.

Therefore, we can write the equation as:

m1 = ρ1 * A1 * V1

Where:
m1 = mass flow rate at state 1
ρ1 = density at state 1
A1 = cross-sectional area at state 1
V1 = velocity at state 1

We are given the mass flow rate at state 2, which is 20.3538 kg/s. We can also find the density at state 2 using the ideal gas law:

P2V2 = mRT2

Where:
P2 = pressure at state 2
V2 = specific volume at state 2
m = mass of gas
R = universal gas constant
T2 = temperature at state 2

By rearranging the equation, we can solve for the specific volume at state 2:

V2 = mRT2/P2

Substituting the given values, we get:

V2 = (20.3538 kg/s * 0.083144 m3/kmol*K * 723.15 K)/6 MPa = 0.199 m3/kg

Now, we can solve for the cross-sectional area at state 1 by using the given information about the inside diameter of the tubes:

A1 = π * (130 mm/2)^2 = 0.013352 m2

Finally, we can rearrange the continuity equation to solve for the inlet velocity at state 1:

V1 = m1/(ρ1 * A1) = 20.3538 kg/s/(ρ1 * 0.013352 m2)

To find the density at state 1, we can use the ideal gas law again:

P1V1 = mRT1

Solving for ρ1, we get:

ρ1 = mRT1/(P1V1)

Substituting the given values, we get:

ρ1 = (20.3538 kg/s * 0.083144 m3/kmol*K * 338.15 K)/(7 MPa *
 
  • #3

v1=2.2781 m^3/kg
velocity1=8.8335 m/s

I would first clarify the context and purpose of this problem. Is it for a specific engineering application or is it a theoretical exercise? This will help determine the appropriate approach and equations to use.

Assuming this is a theoretical exercise, the first thing I would do is apply the principle of mass conservation. Mass cannot be created or destroyed, only transformed. Therefore, the mass flow rate at the inlet (state 1) must be equal to the mass flow rate at the outlet (state 2).

Next, I would use the ideal gas law to calculate the specific volume at state 1. Since the water is entering the tubes at a given pressure and temperature, we can assume it is in a gaseous state. Therefore, we can use the ideal gas law equation:

PV = mRT

Where P is pressure, V is specific volume, m is mass, R is the gas constant, and T is temperature.

We know the values for P, T, and V2 (specific volume at state 2), so we can solve for m, which will give us the mass flow rate at state 1.

Once we have the mass flow rate at state 1, we can use the equation for mass flow rate you provided in your attempt at a solution to calculate the velocity at the inlet.

In summary, to solve this problem, we would use the principles of mass conservation and the ideal gas law to calculate the mass flow rate and velocity at the inlet.
 

1. What is the law of conservation of mass?

The law of conservation of mass, also known as the law of mass conservation, states that the total mass of a closed system will remain constant over time. This means that in any physical or chemical process, the mass of the products must equal the mass of the reactants.

2. How does the law of conservation of mass relate to thermodynamics?

The law of conservation of mass is a fundamental principle in thermodynamics, which is the study of energy and its transformations. In thermodynamics, the law of conservation of mass is often used in conjunction with the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted.

3. What is an example of thermodynamic conservation of mass?

An example of thermodynamic conservation of mass is a combustion reaction, such as burning wood. In this reaction, the mass of the reactants (wood and oxygen) must equal the mass of the products (carbon dioxide and water). This demonstrates the conservation of mass as well as the first law of thermodynamics, as the energy released from the reaction is equal to the energy required to break the bonds in the reactants.

4. Why is the conservation of mass important in scientific research?

The conservation of mass is important in scientific research because it is a fundamental law that must be taken into consideration in all physical and chemical processes. It allows scientists to accurately predict the products of a reaction and understand the energy changes involved. It also provides a basis for understanding the properties and behavior of matter.

5. Is the law of conservation of mass always applicable?

The law of conservation of mass is a fundamental principle in science, but it may not always be applicable in certain scenarios. For example, in nuclear reactions, mass can be converted into energy according to Einstein's famous equation E=mc^2. However, in everyday chemical and physical processes, the law of conservation of mass is a reliable principle that is consistently observed.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
10
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
17
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
470
  • Engineering and Comp Sci Homework Help
Replies
31
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
7K
  • Engineering and Comp Sci Homework Help
Replies
5
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
995
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
3K
Back
Top