1
$\begingroup$

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.

$\endgroup$
  • 1
    $\begingroup$ "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. $\endgroup$ – Gaurang Tandon Dec 21 '17 at 11:59
  • $\begingroup$ 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? $\endgroup$ – jeanne clement Dec 21 '17 at 12:11
  • $\begingroup$ 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. $\endgroup$ – Gaurang Tandon Dec 21 '17 at 12:12
  • $\begingroup$ 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. $\endgroup$ – Gaurang Tandon Dec 21 '17 at 12:17
  • 1
    $\begingroup$ 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 $1004\times10^3.$ $\endgroup$ – David K Dec 21 '17 at 13:06
3
$\begingroup$

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} $

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ great answer. you really helped me. thank you very much $\endgroup$ – jeanne clement Jan 14 '18 at 17:23
  • $\begingroup$ Glad to help! ............................. $\endgroup$ – cgiovanardi Jan 14 '18 at 21:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.