SME
Propulsion · Problem type
Turbofan thrust
Use this for “A turbofan’s core takes 20 kg/s with a bypass ratio of 5 at 230 m/s. The core jet leaves at 500 m/s, the fan jet at 320 m/s. Find its thrust.”
Chart
Core: 5.4 kN
Bypass: 9 kN
Bypass mass flow ṁb = 100 kg/s
This is an example. Type your own values to start a new problem.
Fc (kN)
=
ṁc (kg/s)
×
(
Vc (m/s)
−
V₀ (m/s)
)
Fb (kN)
=
BPR
×
ṁc (kg/s)
×
(
Vb (m/s)
−
V₀ (m/s)
)
F (kN)
=
Fc (kN)
+
Fb (kN)
ṁb
Bypass mass flow
calculated · kg/s
Formulas
ṁb = BPR × ṁc
100 = 5 × 20
Fc
=
ṁc
×
(Vc
−
V₀
)
5,400 = 20 × (500 − 230)
Fb
=
ṁb
×
(Vb
−
V₀
)
9,000 = 100 × (320 − 230)
F
=
Fc
+
Fb
14,400 = 5,400 + 9,000
Formulas are worked in N. The step-by-step shows the conversions.
Assumptions
•
Separate core and fan (bypass) jets, each expanded to the ambient pressure.
•
Bypass ratio BPR: the air through the fan duct over the air through the core, ṁb ÷ ṁc.
•
The fuel’s mass is small beside the air’s and is left out of the momentum.
Step-by-step
WE KNOW
ṁc = 20 kg/s, BPR = 5, V₀ = 230 m/s, Vc = 500 m/s, Vb = 320 m/s
FIND
bypass mass flow (ṁb), core thrust (Fc), bypass thrust (Fb), total thrust (F)
Step 1 · Find bypass mass flow (ṁb)
Use ṁb = BPR × ṁc
The fan moves BPR kilograms past the core for each kilogram through it.
ṁb = 5 × 20
ṁb = 100 kg/s
Step 2 · Find core thrust (Fc)
Use Fc = ṁc × (Vc − V₀)
The core stream’s thrust: its mass flow times the speed it gains.
Fc = 20 × (500 − 230)
Fc = 20 × 270
Fc = 5,400 N
Step 3 · Find bypass thrust (Fb)
Use Fb = ṁb × (Vb − V₀)
The bypass stream’s thrust: its mass flow times the speed it gains.
Fb = 100 × (320 − 230)
Fb = 100 × 90
Fb = 9,000 N
Step 4 · Find total thrust (F)
Use F = Fc + Fb
The two jets push together: add their thrusts.
F
=
5,400
+
9,000
F
=
14,400
N
Step 5 · Convert the answers
Change each answer back to the unit you chose.
Fc = 5,400 N = 5.4 kN (1 kN = 1000 N)
Fb = 9,000 N = 9 kN (1 kN = 1000 N)
F = 14,400 N = 14.4 kN (1 kN = 1000 N)
Check
Put the numbers back in. Both sides should match.
100 = 5 × 20 ✓
5,400 = 20 × (500 − 230) ✓
9,000 = 100 × (320 − 230) ✓
14,400 = 5,400 + 9,000 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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