Compound Hood Assignment

I only need the formulas (not the answers). Please see attached.

Compound Hood Assignment

We have an 8’ by 4’ hopper grate which is used for shakeout in a foundry. The details in the pieces we are casting prevent the use of a totally enclosed ventilation system, so we will design a side draft hood. The side draft hood will control the release of silica from the shells and protect the breathing zone of our employees, while still allowing access to the work during shakeout.

We will need two figures to calculate the ventilation requirements for a side draft shakeout hood. First refer to the figure titled “Foundry Shakeout Side Draft.” This was figure VS-20-02 in older editions of the text. If your text has different nomenclature, go to the index in the back of the book, look up ‘Foundry” and under “Foundry” find ‘Shakeout.”

In the bottom left hand corner you see the statement, “See VS-20-01 for exhaust rates.” Figure VS-20-01 is for enclosed shakeout ventilation, not side draft, but we still must look there to find out how to calculate Q.

We see in the table in figure VS-20-01, the third row is for a “side hood” and refers to VS-20-02. Assume we have cool castings. We see for the side hood and cool castings, we require 350 CFM to 400 CFM per ft2 of grate area. (Page 2-3)

1. What is our grate area in square feet, ft2?

Assume we select 400 CFM / ft2.

2. What is the required volume flow rate, Q?

We now return to figure VS-20-02, which shows the actual compound hood we desire to design. In the upper left corner we see the face of our hood, in the direction of air flow. It shows about 15 vertical slots. It also describes that these slots must be made with moveable panels so that they may be opened or closed. By adjusting the width of these slots after the system is in operation, we can control the flow of exhaust air and make sure we had the desired distribution to capture our contaminant. We also see that our hood must be 1.5 times as long as our grate. Remember our grate was 8 feet long by 4 feet wide. In this diagram, L stands for the greater dimension of our grade (8 ft in this example), and W stands for the lesser dimension (4 ft in this example).

3. How wide must we make our side draft hood?

We see right below the diagram of the hood face, that the velocity through openings (meaning the slots) must be at least 2,000 FPM (feet per minute).

4. Using the Q calculated in question 2, what is the total surface area required for the slots?

You based on this calculation of total slot area, you would determine the number of slots required. This would require some professional intuition. The number of slots and their arrangement cannot just be calculated. You would then each slot accordingly.

In the center of figure VS-20-02, near the bottom, we see “Minimum duct velocity = 4000 FPM.” This tells us the duct transport velocity must be 4,000 FPM (feet per minute) or greater. As with the simple duct, we use the Q calculated above, and this transport velocity calculate a nominal duct area.

5. What cross sectional area of duct would give you exactly a duct velocity of 4,000 FPM if the volume flow rate is that determined above?

6. What would be the diameter of a duct with the surface area calculated above?

Assume we can only buy ducts with an even increment of 2” in diameter at this size.

7. What size duct will you use?

8. What will be the duct velocity for the volume flow rate, Q, calculated above if this diameter of duct is used? Notice, if your result is less than 4,000 FPM, your duct is too large, or you made and error in this calculation.

We see near the bottom of figure VS-20-02 that the hood entry loss, he, will be given by

We denote the slot velocity pressure by VPs and the duct velocity pressure by VPd. We designed for a slot velocity of 2,000 FPM, and we determined our duct velocity in question 8. Remembering that in general

9. Calculate the slot and duct velocity pressures.

10. What is the hood entry loss, he?

This hood entry loss takes us all the way back to the beginning of the duct. We only need this entry loss (due to friction), and VPd (the kinetic energy) to calculate the static pressure required at the beginning of our duct.
11. What static pressure is required at the beginning of the duct to accelerate the air to duct velocity and overcome the pressure losses in this compound hood?

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