Horizontal force exerted by an engine

[theBEAST]

Homework Statement

I am only confused about question 2.

The Attempt at a Solution

I decided to use bernoulli's equation to find velocity at point 1. With velocity at point 1 and point 2 I can use conservation of momentum to solve for the force exerted. In this case there would be Fx, pressure force at 1 and pressure force at 2. However as you can see in my second last and last lines of work, v1 comes out to be an imaginary number which is impossible.

What am I doing wrong?

 

[Esteban]

I think, in the step where you compute the density is wrong, 'cause R's value in the international system of measures is $$R=8,314 \dfrac{J}{mol \cdot K}$$

 

[theBEAST]

I think, in the step where you compute the density is wrong, 'cause R's value in the international system of measures is $$R=8,314 \dfrac{J}{mol \cdot K}$$

The R in this equation refers to the specific gas constant of air, so it isn't 8.3146 I believe.

 

[Esteban]

Oh, lol ahahahha

 

[Nickie]

I would first like to commend you on your approach to the problem and your use of Bernoulli's equation and conservation of momentum. However, it seems that you may have made a mistake in your calculations which resulted in the imaginary number for v1. I suggest double checking your calculations and equations to ensure accuracy. Additionally, it may be helpful to try solving the problem using a different method or approach to see if you get the same result. If you continue to encounter difficulties, I recommend seeking assistance from a colleague or instructor to help identify and correct any errors. As a scientist, it is important to always check and double check our work to ensure accuracy and validity. Good luck with your problem!