steam enters a turbine with a velocity of 16m/s and enthalpy 2950kj/kg . the steam leaves turbine with a velocity 32m/s and specific enthalpy 2539kj/kg. the heat lost to the surroundings as the steam passes through the turbine Is 25kj/kg . the steam flow rate is 32400kg/hr. determine the work output from the turbine in kilowatt.?
To determine the work output from the turbine, we need to calculate the change in specific enthalpy and the mass flow rate of the steam.
Given:
- Initial velocity of steam entering the turbine (v1) = 16 m/s
- Initial specific enthalpy of steam entering the turbine (h1) = 2950 kJ/kg
- Final velocity of steam leaving the turbine (v2) = 32 m/s
- Final specific enthalpy of steam leaving the turbine (h2) = 2539 kJ/kg
- Heat lost to the surroundings (Q) = 25 kJ/kg
- Steam flow rate (m) = 32400 kg/hr
1. Calculate the change in specific enthalpy (Δh) using the formula:
Δh = h1 - h2
Δh = 2950 kJ/kg - 2539 kJ/kg
Δh = 411 kJ/kg
2. Convert the steam flow rate from kilograms per hour to kilograms per second:
m = 32400 kg/hr × (1 hr/3600 s)
m = 9 kg/s
3. Calculate the work output (W) from the turbine using the formula:
W = m × (Δh - Q)
W = 9 kg/s × (411 kJ/kg - 25 kJ/kg)
W = 9 kg/s × 386 kJ/kg
W = 3474 kJ/s
4. Convert the work output from kilojoules per second to kilowatts:
1 kilowatt = 1000 joules/second
W = 3474 kJ/s × (1000 J/1 kJ) × (1 kW/1000 J)
W = 3,474 kW
Therefore, the work output from the turbine is 3,474 kilowatts.
To determine the work output from the turbine, we can use the First Law of Thermodynamics, which states that the change in enthalpy of a system is equal to the heat added to the system minus the work done by the system.
The change in enthalpy (ΔH) of the steam as it passes through the turbine can be calculated using the specific enthalpy values:
ΔH = h2 - h1
where h2 is the specific enthalpy of the steam leaving the turbine and h1 is the specific enthalpy of the steam entering the turbine.
Given:
h1 = 2950 kJ/kg
h2 = 2539 kJ/kg
ΔH = 2539 kJ/kg - 2950 kJ/kg
= -411 kJ/kg
Negative value of ΔH indicates a decrease in enthalpy, which implies that work is done by the system (the turbine).
Now, we need to calculate the mass flow rate of the steam in kg/s. We are given the steam flow rate in kg/hr, so we need to convert it to kg/s:
Steam flow rate = 32400 kg/hr
= 32400 / 3600 kg/s
= 9 kg/s
Next, we can calculate the work output from the turbine using the formula:
Work output = ΔH * mass flow rate * 1000
= -411 kJ/kg * 9 kg/s * 1000
= -3,699,000 kW
The negative sign indicates that work is being extracted from the system. However, this result implies that the turbine is doing work on the surroundings, which is unlikely. Therefore, there might be a mistake in the given information or calculation. Please review the values provided and make sure they are accurate.