How Do You Calculate Airflow and Pressure Changes in a Duct System?

[zakf355]

fluid mechanics question help!?

Homework Statement

Air flows through a horizontal duct of dimensions 300 x 300 mm with a velocity of 15 m/s. At position (1) in the duct a water gauge (water manometer) registers a hieght of 215mm. The duct bends downwards and reduces in size to 240 x 240 mm, dropping a distance of 12 m to position (2). the specific volume of the air is 0.85 m^3 / kg and this may be taken as constant. Determine:

a) volume flow rate and mass flow rate.
b) pressure at (1) in kPa
c) The Velocity at (2)
d) pressure at (2) in kPa (guage) and mm water gauge if losses are neglected.
e) pressure at (2) in kPa (gauge and mm water gauge if losses are 10% of the total head at (1) and elevation (2) is used as datum

Homework Equations

Bernoulli's Equation

mass flow rate = v A relative density

The Attempt at a Solution

im struggling guys

Homework Statement

Homework Equations

The Attempt at a Solution

 

[SteamKing]

I'm not surprised that you're struggling. Are you sure that the water gauge at point 1 reads 215 m? That's a pretty large water gauge, equal to the height of a 70 story building. BTW, atmospheric pressure is about 10 m W.G.

 

[zakf355]

haha its mm. silly me :/

 

[SteamKing]

You've got to show some effort to get help from PFers. That's the rules. "I'm struggling" isn't good enough.

 

[rezeew]

I would suggest breaking down this problem into smaller, more manageable parts. First, let's start by identifying the given information and what is being asked for. We are given the dimensions of a duct, the air velocity, and the height of a water gauge at two positions. We are asked to determine the volume and mass flow rates, pressure at position (1) and (2), and the velocity at position (2).

Next, we can use Bernoulli's equation to solve for the pressure at position (1) and (2). Bernoulli's equation states that the sum of the static pressure, dynamic pressure, and potential energy per unit mass is constant along a streamline. In this case, we can assume that the air is incompressible and that there are no losses. Therefore, we can simplify the equation to P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2, where P is pressure, ρ is density, and v is velocity.

To solve for the volume and mass flow rates, we can use the equation Q = Av, where Q is volume flow rate, A is area, and v is velocity. We are given the dimensions of the duct, so we can calculate the area at position (1) and (2) and then use the given velocity to solve for the volume flow rate. The mass flow rate can be found by multiplying the volume flow rate by the air density.

Using the given specific volume and the calculated volume flow rate, we can solve for the pressure at position (1) in kPa. To find the velocity at position (2), we can use the continuity equation, which states that the volume flow rate is constant along a streamline. Therefore, we can set the volume flow rate at position (1) equal to the volume flow rate at position (2) and solve for the velocity.

To determine the pressure at position (2), we can use the same equation as before, but we need to account for the losses. We are given that the losses are 10% of the total head at position (1) and that the elevation at position (2) is used as the datum. This means that we need to subtract 10% of the total head from the pressure at position (1) to find the pressure at position (2).

I hope this helps with your understanding of this problem