Cubic yards per minute to Cubic Millimeters per second conversion

How to convert cubic yards per minute to cubic millimeters per second?

Sure, let's start by converting 1 cubic yard per minute (yd³/min) to cubic millimeters per second (mm³/s).

First, let's break this down step by step:

Step 1: Conversion Factors

1. 1 yard = 3 feet
2. 1 foot = 12 inches
3. 1 inch = 25.4 millimeters

Step 2: Calculate the Volume Conversion

Since we are dealing with cubic measurements, we need to cube these linear conversion factors:

1. 1 yard = $3 \text{ feet}$
2. $1 \text{ cubic yard} = (3 \text{ feet})^3 = 27 \text{ cubic feet}$
3. $1 \text{ cubic foot} = (12 \text{ inches})^3 = 1,728 \text{ cubic inches}$
4. $1 \text{ cubic inch} = (25.4 \text{ millimeters})^3 = 16,387.064 \text{ cubic millimeters}$

Step 3: Calculate the Total Volume in Cubic Millimeters

Thus, 1 cubic yard is: $1 \text{ yd}^3 = 27 \text{ ft}^3 \times 1,728 \text{ in}^3/\text{ ft}^3 \times 16,387.064 \text{ mm}^3/\text{ in}^3$

$1 \text{ yd}^3 = 27 \times 1,728 \times 16,387.064 \text{ mm}^3$

$1 \text{ yd}^3 = 764,554,857.28 \text{ mm}^3$

Step 4: Convert the Time Units

To convert minutes to seconds: $1 \text{ minute} = 60 \text{ seconds}$

Step 5: Calculate the Volume Flow Rate

Thus, 1 cubic yard per minute to cubic millimeters per second:

$1 \text{ yd}^3/\text{ min} = 764,554,857.28 \text{ mm}^3/60 \text{ s}$ $1 \text{ yd}^3/\text{ min} ≈ 12,742,580.955 \text{ mm}^3/\text{ s}$

Real-World Examples:

1. Construction Site Concrete Pouring:

   • A concrete truck might deliver 3 cubic yards per minute.
   • To find the flow rate in mm³/s: $3 \text{ yd}^3/\text{ min} \times 12,742,580.955 \text{ mm}^3/\text{ s}$ $≈ 38,227,742.865 \text{ mm}^3/\text{ s}$

2. Water Flow in Pipes:

   • A large drainage system might channel water at 0.5 cubic yards per minute.
   • To find the flow rate in mm³/s: $0.5 \text{ yd}^3/\text{ min} \times 12,742,580.955 \text{ mm}^3/\text{ s}$ $≈ 6,371,290.4775 \text{ mm}^3/\text{ s}$

3. Excavation and Earth Moving Equipment:

   • An excavator might displace soil at a rate of 2 cubic yards per minute.
   • To find the flow rate in mm³/s: $2 \text{ yd}^3/\text{ min} \times 12,742,580.955 \text{ mm}^3/\text{ s}$ $≈ 25,485,161.91 \text{ mm}^3/\text{ s}$

These examples give a sense of how significant these flow rates are in practical applications like construction, plumbing, and infrastructure development.