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Grace [21]
3 years ago
10

Liquid water enters a valve at 300 kPa and exits at 275 kPa. As water flows through the valve, the change in its temperature, st

ray heat transfer with the surroundings, and potential energy effects are negli-gible. Operation is at steady state. Modeling the water as incompress-ible with constant rho= 1000 kg/m3, determine the change in kinetic energy per unit mass of water flowing through the valve, in kJ/kg
Engineering
1 answer:
Elan Coil [88]3 years ago
3 0

Answer:

The change in kinetic energy per unit mass of water flowing through the valve is - ΔKE = 0.025 KJ/Kg

Explanation:

Knowing

-Fluid is air

-inlet 1: P1 = 300 kPa

-exit 2: P2 = 275 kPa

density - rho= 1000 kg/m3

Using the formula

Δh = cΔT + Δp/rho

as change in temperature is neglected then change in enthalpy becomes

Δh = Δp/rho

energy equation could be defined by

Q - W = m(out) [h(out) V^{2}(out)/2 + g Z(out)] - m(in) [h(in) V^{2}(in)/2 + g Z(in)]

Q - W = m2 [h2 V^{2}2/2 + g Z2] - m1 [h1 V^{2}1/2 + g Z1]

as for neglecting potential energy effects

Q - W = m2(h2) - m1(h1)

as the system is adiabatic and has no work done

0 = m2 [h2 V^{2}2/2] - m1 [h1 V^{2}1/2]

from mass balance m1 = m2

0 = [h2 V^{2}2/2] - [h1 V^{2}1/2]

Change in kinetic energy could be defined by

ΔKE = V^{2}2/2 - V^{2}1/2

Change in specific enthalpy could be defined by

Δh = h2 - h1

Then the change in kinetic energy per unit mass of water flowing through the valve could be calculated as following

ΔKE = -Δh = ΔP/rho

-(275 - 300)/1000 = 0.025 KJ/Kg

- ΔKE = 0.025 KJ/Kg

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Steam flows steadily through an adiabatic turbine. The inlet conditions of the steam are 10 MPa, 450°C, and 80 m/s, and the exit
8090 [49]

Answer:

a) The change in Kinetic energy, KE = -1.95 kJ

b) Power output, W = 10221.72 kW

c) Turbine inlet area, A_1 = 0.0044 m^2

Explanation:

a) Change in Kinetic Energy

For an adiabatic steady state flow of steam:

KE = \frac{V_2^2 - V_1^2}{2} \\.........(1)

Where Inlet velocity,  V₁ = 80 m/s

Outlet velocity, V₂ = 50 m/s

Substitute these values into equation (1)

KE = \frac{50^2 - 80^2}{2} \\

KE = -1950 m²/s²

To convert this to kJ/kg, divide by 1000

KE = -1950/1000

KE = -1.95 kJ/kg

b) The power output, w

The equation below is used to represent a  steady state flow.

q - w = h_2 - h_1 + KE + g(z_2 - z_1)

For an adiabatic process, the rate of heat transfer, q = 0

z₂ = z₁

The equation thus reduces to :

w = h₁ - h₂ - KE...........(2)

Where Power output, W = \dot{m}w..........(3)

Mass flow rate, \dot{m} = 12 kg/s

To get the specific enthalpy at the inlet, h₁

At P₁ = 10 MPa, T₁ = 450°C,

h₁ = 3242.4 kJ/kg,

Specific volume, v₁ = 0.029782 m³/kg

At P₂ = 10 kPa, h_f = 191.81 kJ/kg, h_{fg} = 2392.1 kJ/kg, x₂ = 0.92

specific enthalpy at the outlet, h₂ = h_1 + x_2 h_{fg}

h₂ = 3242.4 + 0.92(2392.1)

h₂ = 2392.54 kJ/kg

Substitute these values into equation (2)

w = 3242.4 - 2392.54 - (-1.95)

w = 851.81 kJ/kg

To get the power output, put the value of w into equation (3)

W = 12 * 851.81

W = 10221.72 kW

c) The turbine inlet area

A_1V_1 = \dot{m}v_1\\\\A_1 * 80 = 12 * 0.029782\\\\80A_1 = 0.357\\\\A_1 = 0.357/80\\\\A_1 = 0.0044 m^2

3 0
3 years ago
An energy system can be approximated to simply show the interactions with its environment including cold air in and warm air out
Elenna [48]

Answer: The energy system related to your question is missing attached below is the energy system.

answer:

a) Work done = Net heat transfer

  Q1 - Q2 + Q + W = 0

b)  rate of work input ( W ) = 6.88 kW

Explanation:

Assuming CPair = 1.005 KJ/Kg/K

<u>Write the First law balance around the system and rate of work input to the system</u>

First law balance ( thermodynamics ) :

Work done = Net heat transfer

Q1 - Q2 + Q + W = 0 ---- ( 1 )

rate of work input into the system

W = Q2 - Q1 - Q -------- ( 2 )

where : Q2 = mCp T  = 1.65 * 1.005 * 293 = 485.86 Kw

             Q2 = mCp T = 1.65 * 1.005 * 308 = 510.74 Kw

              Q = 18 Kw

Insert values into equation 2 above

W = 6.88 Kw

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2 years ago
What is the function rule for the line? f(x)=−32x−2f(x)=−23x−2f(x)=32x−2f(x)=−32x+2A coordinate grid with x and y axis ranging f
murzikaleks [220]

Answer:

f(x)=23x−2

Explanation:

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At a point on the free surface of a stressed body, the normal stresses are 20 ksi (T) on a vertical plane and 30 ksi (C) on a ho
victus00 [196]

Answer:

The principal stresses are σp1 = 27 ksi, σp2 = -37 ksi and the shear stress is zero

Explanation:

The expression for the maximum shear stress is given:

\tau _{M} =\sqrt{(\frac{\sigma _{x}^{2}-\sigma _{y}^{2}  }{2})^{2}+\tau _{xy}^{2}    }

Where

σx = stress in vertical plane = 20 ksi

σy = stress in horizontal plane = -30 ksi

τM = 32 ksi

Replacing:

32=\sqrt{(\frac{20-(-30)}{2} )^{2} +\tau _{xy}^{2}  }

Solving for τxy:

τxy = ±19.98 ksi

The principal stress is:

\sigma _{x}+\sigma _{y} =\sigma _{p1}+\sigma _{p2}

Where

σp1 = 20 ksi

σp2 = -30 ksi

\sigma _{p1}  +\sigma _{p2}=-10 ksi (equation 1)

\tau _{M} =\frac{\sigma _{p1}-\sigma _{p2}}{2} \\\sigma _{p1}-\sigma _{p2}=2\tau _{M}\\\sigma _{p1}-\sigma _{p2}=32*2=64ksi equation 2

Solving both equations:

σp1 = 27 ksi

σp2 = -37 ksi

The shear stress on the vertical plane is zero

4 0
3 years ago
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