# How to find the power of a jet engine?

I tried much to solve this question but couldn't get answer.

Q. A jet engine consumes 1 kg of fuel for each 40 kg of air intake. Fuel consumption is 1 kg/sec. When aircraft travels in the still air at 200 m/sec, the velocity of discharge gases with respect to engine is 700 m/sec. The power developed by engine is

a) $7200\ kW\quad$ b) $5600\ kW\quad$ c) $2070\ kW\quad$ d) $4140\ kW$

My attempt:

Power of jet engine should be equal to the kinetic energy imparted to the discharge gases per unit time
$$=\frac{1}{2}(\text{mass flow rate of discharge gases})(\text{relative velocity of gases})^2$$ $$=\frac12(\dot m)(V_r)^2$$$$=\frac12(1+40)(700)^2\ J/sec$$$$=1004\ kW$$

My answer is not matching with any option. Can somebody please help me or suggest me where I am wrong? Thanks you very much.

• "classical-mechanics" For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question. Please read the tag description carefully. I think this is a more physics oriented question, and unsuited for this site. – Gaurang Tandon Dec 21 '17 at 11:59
• yes, but they don't give answer to such question I don't know why. Can you please give me some hint to solve it? – jeanne clement Dec 21 '17 at 12:11
• If you mean by "they", the physics stackexchange community. Then you should read their policy of admissible questions before asking. They don't appreciate "check-my-work" questions I believe. Let me see what's wrong with your work. – Gaurang Tandon Dec 21 '17 at 12:12
• I tried to solve your problem. I think the answer should be $1/2\cdot \text{mass of gases discharged}\cdot \text{velocity of discharged gases wrt ground}^2$. So, the $v$ should be $700-200=500$. Although, it also does not match with the options. I believe, in the question, the mass of discharged gases is unclear. PS: While I appreciate your well-formed question and have given it an upvote, I have also flagged it as off-topic for the site, as it is. – Gaurang Tandon Dec 21 '17 at 12:17
• Aside from the issues about which numbers got plugged into the formula, there's an arithmetic error between the last two lines of the equation in the question: $\frac12(1+40)700^2 = 10045\times10^3,$ not $1004\times10^3.$ – David K Dec 21 '17 at 13:06

The net force is:

$\text{Net force} = ( \dot m \cdot v)_{out} - ( \dot m \cdot v)_{in}$

$\text{Net force} = ( 41 \cdot 700)_{out} - ( 40 \cdot 200)_{in}$

$\text{Net force} = 28700 - 8000$

$\text{Net force} = 20700 \text{N}$

**

The power developed is:

$\text{Power} = \text{Net force} \cdot \text{Plane velocity}$

$\text{Power} = 20700 \text{N} \cdot 200 \text{m/s}$

$\text{Power} = 4140 \text{kW}$

• great answer. you really helped me. thank you very much – jeanne clement Jan 14 '18 at 17:23
• Glad to help! ............................. – cgiovanardi Jan 14 '18 at 21:16