EGR 334 Thermodynamics: Homework 16Problem 4:36Methane (CH4) gas enters a horizontal well insulated nozzle operating at steady state at 80 deg. C and a velocity of 10 m/s. Assuming ideal gas behavior for the methane, plot the temperature of the gas exiting the nozzle in deg C versus the exit velocity ranging from 500 to 600 m/s.-------------------------------------------------------------------------------------------------------------------------------------------Methane as ideal gasState 1: T1 = 80 C= 353 K V1 = 10 m/sState 2: V2 = 500 to 600 m/s

Energy Balance for a Nozzle at steady state:

assuming: no work, no heat loss, constant elevation.

Using ideal gas model:

do unit check:

cp can be found from table A-21 where

where so

A plot of the T2 vs V2 is shown on the next page which was created using Excel:

Plot of T2 vs. V2 for nozzle.

or solved with IT

x

EGR 334 Thermodynamics: Homework 16Problem 4:43Air expands through a turbine from 8 bar, 960 K to 1 bar, 450 K. The inlet velocity is small compared to the exit velocity of 90 m/s. The turbine operates at steady state and develops a power output of 2500 kW. Heat transfer between the turbine and its surroundings and potential energy effects are negligible. Modeling air as an ideal gas, calculate the mass flow rate of air in kg/s and the exit area in sq. m.----------------------------------------------------------------------------------------------------------------------------------Turbine using air as ideal gas State 1: p1 = 8 bar and T1 = 960 K V1 << V2 = 90 m/sState 2: p2 = 1 bar, and T2= 450 KTurbine power =Wdot = 2500 kW Assume: Q = 0 and ΔPE = 0

constants: use R = 0.2870 kJ/kg-K cp(@700K) = 1.075 kJ/kg-K

Using ideal gas: State 1:

State 2:

from the energy balance at steady state:

Assume Q = 0 and ΔPE = 0

from the mass balance at steady state:

Volumetric flow rate is given by

and

EGR 334 Thermodynamics: Homework 16Problem 4:52Air enters a compressor operating at steady state at 1 atm with a specific enthalpy of 290 kJ/kg and exits at a higher pressure with a specific enthalpy of 1023 kJ/kg. The mass flow rate is 0.1 kg/s. If the compressor power input is 77 kW, determine the rate of heat transfer between the compressor and its surroundings, in kW. Neglect kinetic and potential energy effects and assume the ideal gas model.------------------------------------------------------------------------------------------------------------------------------Air at steady state as an ideal gas: mdot = 0.1 kg/s W compressor in = 77 kWp1 = 1 atm h1 = 290 kJ/kgp2 > p1 h2 = 1023 kJ/kgconstants: use R = 0.2870 kJ/kg-K

Assume V1≈V2 and ΔPE = 0

for Air as ideal gas, T can be found from table A-22: for h1 = 290 kJ/kg……T1 = 289.8 K h2 = 1023kJ/kg……T2 = 979.8 K

from the mass balance at steady state:

from the energy balance at steady state:

Assume V1≈V2 and ΔPE = 0

EGR 334 Thermodynamics: Homework 16Problem 4:66The figure provides steady state operating data for a pump drawing water from a reservoir and delivering it at a pressure of 3 bar to a storage tank perched above the reservoir. The mass flow rate of the water is 1.5 kg/s. The water temperature remains nearly constant at 15 deg C, there is no significant change in kinetic energy from inlet to exit and heat transfer between the pump and its surroundings is small. Determine the power required by the pump in kW. Let g = 9.81 m/s2.---------------------------------------------------------------------------------------------------------------------------------State 1: T1 = 15 C p1 = 1bar z1 = 0 state 2: T2 = 15 C p2 = 3 bar z2 =15 m

Assume ΔKE = 0 and Q = 0

Steady state:from the mass balance at steady state:

from the energy balance at steady state:

Assume Q = 0 and ΔKE = 0 for liquid h1 = h2 = hf(T=15) if temperature is constant

The work is negative since is done on the system which the work that needs to be done by the pump on the system:

Alternate solution: Using equation 3.13:

where

= -0.521 kW