All categories

3 years ago

Which Reynolds number would (most likely) correspond to a system where radial variations in velocity were negligible

1 answer:

3 0

Three different cases are computed to clarify the possible influence of the jet Reynolds number. The Reynolds number Re = V0e/ν is set to 3000 for case (I), 7500 for case (II) and 13500 for case (III). The nondimensional time step ΔtV0/e is fixed to a value which ensure the stability of the numerical scheme (CFL< 0.3). For the largest Reynolds number simulation (Re = 13500), we have to mention that only mean quantities are here reported since insufficient integration times are yet available for this case.
The length of the horizontal direction must be large enough to capture the two large recirculations on each side of jet and to limit the influence of the buffer domain inside of the domain of interest. Preliminary bidimensional simulations have been used to test the influence of the length of the horizontal direction. We concluded that a value of Hx/e = 40 is sufficient. In the framework of air curtain applications, the opening ratio is fixed to 10 for all cases. The choice of the length of the homogeneous direction (Oz) is less obvious. Indeed, the periodic boundary conditions along the homogeneous direction are justified only if the transverse dimension Hz is large enough to capture the largest structures of the flow. Consequently, the fluctuations must be practically decorrelated on a half-period (Hz/2). In the absence of two point correlations available in the literature for plane jets with short impingement distance, we considered successively two different transverse dimensions: Hz/e = π in accordance with the simulations of Hoffmann and Benocci (1994); Voke et al. (1995), then a double dimension Hz/e = 2π. Note that Cziesla et al. (2001) set the length of the homogeneous direction to 2. Beaubert and Viazzo (2001) note an overlapping problem on the transverse two-point correlations of the different velocity components in the plane of symmetry of the jet for the smallest width. Therefore, a width of 2π for the transverse direction is rather advised for the ratio Hy/e = 10 and in this range of Reynolds numbers. Table 1 contains the characteristics of the three simulations.

You might be interested in

Convert the improper fraction to a mixed number

Yuliya22 [10]

Answer:

18. 24/8 = 3

19. 50/12 = 4 and one-sixth

20. 18/16 = 1 and one-eighth

Explanation: I’m good at math

4 0

3 years ago

Read 2 more answers

A power washer is being used to clean the siding of a house. Water enters at 20 C, 1 atm, with a velocity of 0.2 m/s .A jet of w

BabaBlast [244]

A power washer is being used to clean the siding of a house. Water at the rate of 0.1 kg/s enters at 20°c and 1 atm, with the velocity 0.2m/s. The jet of water exits at 23°c, 1 atm with a velocity 20m/s at an elevation of 5m. At steady state, the magnitude of the heat transfer rate from power unit to the surroundings is 10% of the power input. Determine the power input to the motor in kW.

Answer:

Net power of 1.2 KW is being extracted

Explanation:

We are given;

Mass flow rate; m' = 0.1kg/s

Inlet temperature; T1 = 20°C = 293K

Inlet pressure; P1 = 1 atm = 10^(5) pa

Inlet velocity; v1 = 0.2 m/s

Exit Pressure; P2 = 1 atm = 10^(5) pa

Exit Temperature; T2 = 1 atm = 296K

Exit velocity; V2 = 20m/s

Change in elevation; h = Z2 - Z1 = 5m

We are told that the magnitude of the heat transfer rate from the power unit to the surroundings is 10% of the power input.

Thus;

Q = -0.1W

From Bernoulli equation;

Q - W = ∆Potential energy + ∆Kinetic energy + ∆Pressure energy

Where;

∆Potential energy = mg(z2 - z1)

∆Kinetic energy = ½m(v2² - v1²)

∆Pressure energy = mc_p(T2 - T1)

Thus;

-0.1W - W = [m'g(z2 - z1)] + [½m'(v2² - v1²)] + [m'c_p(T2 - T1)]

Where C_p is specific heat capacity of water = 4200 J/Kg.k

Plugging in the relevant values, we have;

-1.1W = (0.1 × 9.81 × 5) + (½ × 0.1(20² - 0.2²)) + (0.1 × 4200 × (296 - 293))

-1.1W = 4.905 + 19.998 + 1260

-1.1W = 1284.903

W = -1284.903/1.1

W ≈ -1168 J/s ≈ -1.2 KW

The negative sign means that work is extracted from the system.

7 0

3 years ago

Consider a very long rectangular fin attached to a flat surface such that the temperature at the end of the fin is essentially t

kodGreya [7K]

Answer:

$\frac{T-20}{130-20}= e^{-14.28*0.05}$

And if we solve for T we got:

$T= 20 + 110e^{-14.28*0.05} = 73.86 C$

The answer for this case would be $T = 73.86 C$ at 5cm from the base of the fin.

Explanation:

Data given

For this case we have the following data given:

$h = 20 \frac{W}{m^2 K}$ represent the heat transfer coefficient.

$p$ represent the perimeter for this case and would be given by:

$p = 2*0.05m +2*0.001m= 0.102m$

$k = 200 \frac{W}{m C}$ represent the thermal conductivity

$w = 5cm =0.05 m$ represent the width

$h = 1mm =0.001m$ represent the thickness

$A= wh= 0.05m *0.001m = 0.00005 m^2$

Solution to the problem

For this case we assume that we have steady conditions, the temperature of the fins varies just in one direction, the heat transfer coefficient not changes with the time and the thermal properties of the fin not change.

We can determine the temperature if the fin at x=5 cm=0.05 m from the base with the following formula:

$\frac{T-T_{\infty}}{T_b -T_{\infty}} = e^{-mx}$

Where m is a coefficient given by:

$m = \sqrt{\frac{hp}{kA}}=\sqrt{\frac{20 W/m^2 C 0.102 m}{200 W/ mC 0.00005 m^2}}= 14.28 m^{-1}$

The value of x for this case represent the distance $x =5 cm =0.05m$

$T_b =130 C$ represent the base temperature

$T_{\infty}= 20$ represent the temperature of the sorroundings or the ambient.

If we replace we have this:

$\frac{T-20}{130-20}= e^{-14.28*0.05}$

And if we solve for T we got:

$T= 20 + 110e^{-14.28*0.05} = 73.86 C$

The answer for this case would be $T = 73.86 C$ at 5cm from the base of the fin.

3 0

3 years ago

What is "Engineering"?

Liono4ka [1.6K]

Engineering is when both the application of science and math are used to solve problems. An engineer is a person who designs, builds, or maintains engines, machines, or public works. There are six large branches of engineering such as Mechanical, Chemical, Civil, Electrical, Management, and Geotechnical, they all have hundreds of subcategories of engineering under each different branch.

5 0

3 years ago

This method will sell the seat in row i and column j unless it is already sold. A ticket is sold if the price of that seat in th

blsea [12.9K]

Answer:

The solution code is written in Java.

public class Movie {
private double [][] seats = new double[5][5];
private double totalSales;
public Movie(){
for(int i= 0; i < this.seats.length; i++){
for(int j = 0; j < this.seats[i].length; j++){
this.seats[i][j] = 12;
}
}
this.totalSales = 0;
}
public boolean bookSeat(int i, int j)
{
if(this.seats[i][j] != 0){
this.totalSales += this.seats[i][j];
this.seats[i][j] = 0;
return true;
}else{
return false;
}
}
}

Explanation:

The method, bookSeat(), as required by the question is presented from Line 16 - 26 as part of the public method in a class Movie. This method take row, i, and column, j, as input.

By presuming the seats is an two-dimensional array with all its elements are initialized 12 (Line 7 - 10). This means we presume the movie ticket price for all the seats are $12, for simplicity.

When the bookSeat() method is invoked, it will check if the current price of seats at row-i and column-i is 0. If not, the current price, will be added to the totalSales (Line 19) and then set the price to 0 (Line 20) and return true since the ticket is successfully sold (Line 21). If it has already been sold, return false (Line 23).

8 0

3 years ago