The specific kinetic energy of a moving mass is given by the formula:
\[ KE = \frac{v^2}{2} \]
where \( v \) is the velocity of the mass. To determine the specific kinetic energy of a mass whose velocity is 100 ft/s in BTU/lbm, follow these steps:
1. **Convert the velocity from ft/s to ft²/s²:**
\( v = 100 \, \text{ft/s} \)
\( v^2 = (100)^2 = 10,000 \, \text{ft}^2/\text{s}^2 \)
2. **Calculate the specific kinetic energy in ft²/s²:**
\( KE = \frac{10,000}{2} = 5,000 \, \text{ft}^2/\text{s}^2 \)
3. **Convert the specific kinetic energy from ft²/s² to BTU/lbm:**
– 1 BTU = 778.169 ft·lbf
– 1 lbf = 32.174 lbm·ft/s²
– Therefore, 1 BTU = 778.169 × 32.174 lbm·ft²/s²
– 1 BTU = 25,037 lbm·ft²/s²
\( KE = \frac{5,000}{25,037} \approx 0.1997 \, \text{BTU/lbm} \)
So, the specific kinetic energy of a mass moving at 100 ft/s is approximately **0.1997 BTU/lbm**.