1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tatiyna
3 years ago
10

Air enters the compressor of a cold air-standard Brayton cycle with regeneration and reheat at 100 kPa, 300 K, with a mass flow

rate of 6 kg/s. The compressor pressure ratio is 10, and the inlet temperature for each turbine stage is 1400 K. The pressure ratios across each turbine stage are equal. The turbine stages and compressor each have isentropic efficiencies of 80% and the regenerator effectiveness is 80%. For k= 1.4.
Calculate:
a. the thermal efficiency of the cycle.
b. the back work ratio.
c. the net power developed, in kW.
Engineering
1 answer:
yanalaym [24]3 years ago
3 0

Answer:

a. 47.48%

b. 35.58%

c. 2957.715 KW

Explanation:

T_2 =T_1 + \dfrac{T_{2s} - T_1}{\eta _c}

T₁ = 300 K

\dfrac{T_{2s}}{T_1} = \left( \dfrac{P_{2}}{P_1} \right)^{\dfrac{k-1}{k} }

T_{2s} = 300 \times (10) ^{\dfrac{0.4}{1.4} }

T_{2s} = 579.21 K

T₂ = 300+ (579.21 - 300)/0.8 = 649.01 K

T₃ = T₂ + \epsilon _{regen}(T₅ - T₂)

T₄ = 1400 K

Given that the pressure ratios across each turbine stage are equal, we have;

\dfrac{T_{5s}}{T_4} = \left( \dfrac{P_{5}}{P_4} \right)^{\dfrac{k-1}{k} }

T_{5s} = 1400×\left( 1/\sqrt{10}  \right)^{\dfrac{0.4}{1.4} }  = 1007.6 K

T₅ = T₄ + (T_{5s} - T₄)/\eta _t = 1400 + (1007.6- 1400)/0.8 = 909.5 K

T₃ = T₂ + \epsilon _{regen}(T₅ - T₂)

T₃ = 649.01 + 0.8*(909.5 - 649.01 ) = 857.402 K

T₆ = 1400 K

\dfrac{T_{7s}}{T_6} = \left( \dfrac{P_{7}}{P_6} \right)^{\dfrac{k-1}{k} }

T_{7s} = 1400×\left( 1/\sqrt{10}  \right)^{\dfrac{0.4}{1.4} }   = 1007.6 K

T₇ = T₆ + (T_{7s} - T₆)/\eta _t = 1400 + (1007.6 - 1400)/0.8 = 909.5 K

a. W_{net \ out} = cp(T₆ -T₇) = 1.005 * (1400 - 909.5) = 492.9525 KJ/kg

Heat supplied is given by the relation

cp(T₄ - T₃) + cp(T₆ - T₅) = 1.005*((1400 - 857.402) + (1400 - 909.5)) = 1038.26349 kJ/kg

Thermal efficiency of the cycle = (Net work output)/(Heat supplied)

Thermal efficiency of the cycle = (492.9525 )/(1038.26349 ) =0.4748 = 47.48%

b. bwr = \dfrac{W_{c,in}}{W_{t,out}}

bwr = (T₂ -T₁)/[(T₄ - T₅) +(T₆ -T₇)]  = (649.01 - 300)/((1400 - 909.5) + (1400 - 909.5)) = 35.58%

c. Power = 6 kg *492.9525 KJ/kg  = 2957.715 KW

You might be interested in
Two substances, A and B, initially at different temperatures, come into contact and reach thermal equilibrium. The mass of subst
Kaylis [27]

Answer:

The specific heat capacity of substance A is 1.16 J/g

Explanation:

The substances A and B come to a thermal equilibrium, therefore, the heat given by the hotter substance B is absorbed by the colder substance A.

The equation becomes:

Heat release by Substance B = Heat Gained by Substance A

The heat can be calculated by the formula:

Heat = mCΔT

where,

m = mass of substance

C = specific heat capacity of substance

ΔT = difference in temperature of substance

Therefore, the equation becomes:

(mCΔT) of A = (mCΔT) of B

<u>FOR SUBSTANCE A:</u>

m = 6.01 g

ΔT = Final Temperature - Initial Temperature

ΔT = 46.1°C - 20°C = 26.1°C

C = ?

<u>FOR SUBSTANCE B:</u>

m = 25.6 g

ΔT = Initial Temperature - Final Temperature

ΔT = 52.2°C - 46.1°C = 6.1°C

C = 1.17 J/g

Therefore, eqn becomes:

(6.01 g)(C)(26.1°C) = (25.6 g)(1.17 J/g)(6.1°C)

C = (182.7072 J °C)/(156.861 g °C)

<u>C = 1.16 J/g</u>

5 0
3 years ago
A tool used to put a concave edge on a plane iron is
tigry1 [53]

Answer:

C) grinder

Explanation:

7 0
2 years ago
Read 2 more answers
A polyethylene rod exactly 10 inches long with a cross-sectional area of 0.04 in2 is used to suspend a weight of 358 lbs-f (poun
Nadya [2.5K]

Answer:

Final length of the rod = 13.90 in

Explanation:

Cross Sectional Area of the polythene rod, A = 0.04 in²

Original length of the polythene rod, l = 10 inches

Tensile modulus for the polymer, E = 25,000 psi

Viscosity, \eta = 1*10^{9} psi -sec

Weight = 358 lbs - f

time, t = 1 hr = 3600 sec

Stress is given by:

\sigma = \frac{Force}{Area} \\\sigma = \frac{358}{0.04} \\\sigma = 8950 psi

Based on Maxwell's equation, the strain is given by:

strain = \sigma ( \frac{1}{E} + \frac{t}{\eta} )\\Strain = 8950 ( \frac{1}{25000} + \frac{3600}{10^{9} } )\\Strain = 0.39022

Strain = Extension/(original Length)

0.39022 = Extension/10

Extension = 0.39022 * 10

Extension = 3.9022 in

Extension = Final length - Original length

3.9022 =  Final length - 10

Final length = 10 + 3.9022

Final length = 13.9022 in

Final length = 13.90 in

7 0
3 years ago
(SI units) Molten metal is poured into the pouring cup of a sand mold at a steady rate of 400 cm3/s. The molten metal overflows
maxonik [38]

Answer:

diameter of the sprue at the bottom is 1.603 cm

Explanation:

Given data;

Flow rate, Q = 400 cm³/s

cross section of sprue: Round

Diameter of sprue at the top d_{top} = 3.4 cm

Height of sprue, h = 20 cm = 0.2 m

acceleration due to gravity g = 9.81 m/s²

Calculate the velocity at the sprue base

V_{base} = √2gh

we substitute

V_{base} = √(2 × 9.81 m/s² × 0.2 m )

V_{base} = 1.98091 m/s

V_{base} = 198.091 cm/s

diameter of the sprue at the bottom will be;

Q = AV = (πd_{bottom}^2/4) × V_{base}

d_{bottom} = √(4Q/πV_{base})

we substitute our values into the equation;

d_{bottom} = √(4(400 cm³/s) / (π×198.091 cm/s))

d_{bottom}  = 1.603 cm

Therefore, diameter of the sprue at the bottom is 1.603 cm

6 0
2 years ago
A metal crystallizes with a face-centered cubic lattice. The edge of the unit cell is 408 pm. Calculate the number of atoms in t
uysha [10]

Answer:288 pm

Explanation:

Number of atoms(s) for face centered unit cell -

Lattice points: at corners and face centers of unit cell.

For face centered cubic (FCC), z=4.

- whereas

For an FCC lattices √2a =4r =2d

Therefore d = a/√2a = 408pm/√2a= 288pm

I think with this step by step procedure the, the answer was clearly stated.

8 0
3 years ago
Other questions:
  • we want to make a schottky diode on one surface of an n-type semiconductor, and an ohmic contact on the other side. the electron
    10·1 answer
  • How much heat (Btu) is prod uced by a 150-W light bulb that is on for 20-hours?
    14·1 answer
  • Technician A says if the input signal turn-on time is too fast for the input circuit, your program may operate as though the inp
    11·1 answer
  • The beam is supported by a pin at A and a roller at B which has negligible weight and a radius of 15 mm. If the coefficient of s
    7·1 answer
  • Can U lose a rank in Brainly by using too many points?
    6·1 answer
  • You are hired as the investigators to identify the root cause and describe what should have occurred based on the following info
    9·1 answer
  • Fluid systems can distribute pressure unequally to all points in a system.<br><br> True<br> False
    15·1 answer
  • Calculate the percentage of recyclables in high socioeconomic localities.
    13·1 answer
  • In the situation shown below, what would the Moon look like from Earth? Sun, Earth and Moon Four Moon Views A. View A B. View B
    8·1 answer
  • Tech A says you can find the typical angle of a V-block engine by dividing the number of cylinders by 720
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!