Using the following tables: Problem 1. (Total 10 pts) You have a large tank of s

Question

Using the following tables:

Problem 1. (Total 10 pts) You have a large tank of stationary air with stagnation temperature To = 305 K and stagnation pressure Po (which we will leave unspecified for now). Air flows out of the tank through the converging nozzle pictured below, into surroundings having pressure = 101.3 kPa. The nozzle has exit area Ae-1.25-10-5 m2. (In this problem use the tables in the Appendix using linear interpolation as necessary.) Ps mX (a) (4 pts) Your goal is to make the air temperature in the exit plane of the nozzle, which we'll call Te, as low as possible. What is that minimum value of Te? What value, or range of values, of the tank pressure, Po, do we need to achieve that temperature? (b) (6 pts) Suppose that po is set so that the exit plane static pressure, Pe, is exactly equal to ps. What's the momentum flow rate (in units of Newtons) of air out of the nozzle exit?

Explanation / Answer

Let To represent stagnation temperature

Po stagnation pressure

T temperature at throat

P pressure at throat

a) Assuming reversible adiabatic flow

Then minimum temperature corresponds to Mach no.= 1

To = 305K

From tables

To/T = 1.2 for M=1

T= To/1.2

Solving the above we get

T= 254.166K

If Po is the corresponding pressure in tank then

Po/Ps =1.8929 ( since in first part exit pressure is not given so assuming atmospheric pressure to be nozzle exit pressure)

Where Ps=101.3kPa (given)

Solving we get Po= 191.7507 kPa

Tank pressure should be equal to 191.7507kPa

b) For nozzle exit pressure equal to atmospheric pressure

Momentum flow rate = Pressure at throat × area at throat

= Ps × A

= 101.3 ×10^3 ×1.25 × 10^(-5) N

=126.25 × 10^(-2) N

= 1.2625 N

  

  

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