How to Determine mdot1 and mdot3?

[bellahyc]

Homework Statement

Please refer to Attached diagram. Find mdot1 and mdot3.

Homework Equations

Ideal gas law...P=density*R*T
mass flow rate equation:mdot=density*area*velocity
mdot3=mdot1+mdot2

The Attempt at a Solution

I assumed the LP gas and the motive gas to be ideal gas, and found the relative densities using ideal gas law...

But it seems to me that it's not possible to find the mass flow rate without a velocity... I tried to find out the speed of sound for inlet motive gas to figure out the velocity but the there's not enough information to figure out the Mach number...I have the gas composition for the motive gas and the LP gas...but not for the HP gas...if you think those information is helpful I will post it up. Can anyone help me out? Thanks a ton :-)

 

[KataKoniK]

Hi there! Thank you for posting your question. I think I can help you with finding mdot1 and mdot3.

First, let's start by defining some variables. Let's say the inlet motive gas has a density of ρ1, velocity of v1, and area of A1. Similarly, the LP gas has a density of ρ2, velocity of v2, and area of A2. Lastly, the HP gas has a density of ρ3, velocity of v3, and area of A3.

Now, using the mass flow rate equation, we can write:

mdot1 = ρ1 * A1 * v1
mdot2 = ρ2 * A2 * v2
mdot3 = ρ3 * A3 * v3

We also know that mdot3 = mdot1 + mdot2. Therefore, we can write:

ρ3 * A3 * v3 = ρ1 * A1 * v1 + ρ2 * A2 * v2

Now, we have three unknowns (mdot1, mdot3, and v3) and three equations. We can solve for these unknowns by using the ideal gas law for each gas:

P1 = ρ1 * R * T1
P2 = ρ2 * R * T2
P3 = ρ3 * R * T3

where P1, P2, and P3 are the pressures of the inlet motive gas, LP gas, and HP gas respectively, and T1, T2, and T3 are their corresponding temperatures.

We also know that P3 = P1 + P2. Substituting the ideal gas law equations, we get:

ρ3 * R * T3 = (ρ1 * R * T1) + (ρ2 * R * T2)

Solving for ρ3, we get:

ρ3 = (ρ1 * T1 + ρ2 * T2) / T3

Substituting this into our mass flow rate equation, we get:

ρ1 * A1 * v1 + ρ2 * A2 * v2 = [(ρ1 * T1 + ρ2 * T2) / T3] * A3 * v3

Now, we have two unknowns (mdot1 and v3) and two equations. We can solve for