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Cubic Millimeters per second (mm³/s) to Cubic yards per hour (yd³/h) conversion

Cubic Millimeters per second to Cubic yards per hour conversion table

Cubic Millimeters per second (mm³/s)	Cubic yards per hour (yd³/h)
0	0
1	0.000004708617735091
2	0.000009417235470183
3	0.00001412585320527
4	0.00001883447094037
5	0.00002354308867546
6	0.00002825170641055
7	0.00003296032414564
8	0.00003766894188073
9	0.00004237755961582
10	0.00004708617735091
20	0.00009417235470183
30	0.0001412585320527
40	0.0001883447094037
50	0.0002354308867546
60	0.0002825170641055
70	0.0003296032414564
80	0.0003766894188073
90	0.0004237755961582
100	0.0004708617735091
1000	0.004708617735091

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

Here's how to convert between cubic millimeters per second ( $mm^3/s$ ) and cubic yards per hour ( $yd^3/hr$ ), along with some context and examples.

Understanding the Conversion

Converting between cubic millimeters per second and cubic yards per hour involves understanding the relationships between metric and imperial units and time. We'll start by outlining the conversion factors.

Conversion Factors

The key conversion factors are:

1 meter (m) = 1.09361 yards (yd)
1 meter (m) = 1000 millimeters (mm)
1 hour (hr) = 3600 seconds (s)

Converting Cubic Millimeters per Second to Cubic Yards per Hour

To convert $mm^3/s$ to $yd^3/hr$ , follow these steps:

Convert $mm^3$ to $m^3$ : Since 1 m = 1000 mm, then $1 m^3 = (1000 mm)^3 = 10^9 mm^3$ . Therefore, $1 mm^3 = 10^{-9} m^3$ .
Convert $m^3$ to $yd^3$ : Since 1 m = 1.09361 yd, then $1 m^3 = (1.09361 yd)^3 \approx 1.30795 yd^3$ .
Convert seconds to hours: 1 hour = 3600 seconds, so $1 s = \frac{1}{3600} hr$ .

Now, combine these conversions:

1 \frac{mm^3}{s} = 1 \frac{mm^3}{s} \times \frac{10^{-9} m^3}{1 mm^3} \times \frac{1.30795 yd^3}{1 m^3} \times \frac{3600 s}{1 hr}

1 \frac{mm^3}{s} = 1 \times 10^{-9} \times 1.30795 \times 3600 \frac{yd^3}{hr}

1 \frac{mm^3}{s} \approx 4.70862 \times 10^{-6} \frac{yd^3}{hr}

Therefore, 1 cubic millimeter per second is approximately $4.70862 \times 10^{-6}$ cubic yards per hour.

Converting Cubic Yards per Hour to Cubic Millimeters per Second

To convert $yd^3/hr$ to $mm^3/s$ , we reverse the process:

Convert $yd^3$ to $m^3$ : Since $1 m^3 = 1.30795 yd^3$ , then $1 yd^3 = \frac{1}{1.30795} m^3 \approx 0.76455 m^3$ .
Convert $m^3$ to $mm^3$ : Since $1 m^3 = 10^9 mm^3$ , then $1 mm^3 = 10^{-9} m^3$ .
Convert hours to seconds: 1 hour = 3600 seconds, so $1 hr = 3600 s$ .

Now, combine these conversions:

1 \frac{yd^3}{hr} = 1 \frac{yd^3}{hr} \times \frac{0.76455 m^3}{1 yd^3} \times \frac{10^9 mm^3}{1 m^3} \times \frac{1 hr}{3600 s}

1 \frac{yd^3}{hr} = 1 \times 0.76455 \times 10^9 \times \frac{1}{3600} \frac{mm^3}{s}

1 \frac{yd^3}{hr} \approx 212375 \frac{mm^3}{s}

Therefore, 1 cubic yard per hour is approximately $212375$ cubic millimeters per second.

Base 10 vs Base 2

This conversion does not depend on base 10 or base 2. It's a direct unit conversion based on the definitions of length and time.

Real-World Examples

While the direct conversion between $mm^3/s$ and $yd^3/hr$ isn't commonly used in everyday scenarios, the principles are applicable. Here are some relevant examples:

Fluid Flow in Microfluidics: In microfluidic devices (used in labs for chemical and biological analysis), flow rates are often measured in $mm^3/s$ (also equivalent to microliters per second, $\mu L/s$ ).
Wastewater Treatment: Flow rates of wastewater in large treatment plants might be measured in cubic yards per hour, representing the total volume of water processed.
HVAC Systems: Airflow in ventilation systems can be quantified in cubic feet per minute (CFM), which can then be related to other volume flow rate units. For example, converting CFM to $yd^3/hr$ or $mm^3/s$ could be relevant for comparison or system design.

See below section for step by step unit conversion with formulas and explanations. Please refer to the table below for a list of all the Cubic yards per hour to other unit conversions.

What is Cubic Millimeters per Second?

Cubic millimeters per second ( $mm^3/s$ ) is a unit of volumetric flow rate, indicating the volume of a substance passing through a specific area each second. It's a measure of how much volume flows within a given time frame. This unit is particularly useful when dealing with very small flow rates.

Formation of Cubic Millimeters per Second

The unit $mm^3/s$ is derived from the base units of volume (cubic millimeters) and time (seconds).

Cubic Millimeter ( $mm^3$ ): A cubic millimeter is a unit of volume, representing a cube with sides that are each one millimeter in length.
Second (s): The second is the base unit of time in the International System of Units (SI).

Combining these, $mm^3/s$ expresses the volume in cubic millimeters that flows or passes through a point in one second.

Flow Rate Formula

The flow rate ( $Q$ ) can be defined mathematically as:

Q = \frac{V}{t}

Where:

$Q$ is the flow rate ( $mm^3/s$ ).
$V$ is the volume ( $mm^3$ ).
$t$ is the time (s).

This formula indicates that the flow rate is the volume of fluid passing through a cross-sectional area per unit time.

Applications and Examples

While $mm^3/s$ might seem like a very small unit, it's applicable in several fields:

Medical Devices: Infusion pumps deliver medication at precisely controlled, often very slow, flow rates. For example, a pump might deliver insulin at a rate of 5 $mm^3/s$ .
Microfluidics: In microfluidic devices, used for lab-on-a-chip applications, reagents flow at very low rates. Reactions can be studied using flow rates of 1 $mm^3/s$ .
3D Printing: Some high resolution 3D printers using resin operate by very slowly dispensing material. The printer can be said to be pushing out material at 2 $mm^3/s$ .

Relevance to Fluid Dynamics

Cubic millimeters per second relates directly to fluid dynamics, particularly in scenarios involving low Reynolds numbers, where flow is laminar and highly controlled. This is essential in applications requiring precision and minimal turbulence. You can learn more about fluid dynamics at Khan Academy's Fluid Mechanics Section.

What is cubic yards per hour?

What is Cubic yards per hour?

Cubic yards per hour (yd³/hr) is a unit of volume flow rate, representing the volume of a substance that passes through a given area per unit of time. Specifically, it measures how many cubic yards of a substance flow in one hour. It's commonly used in industries dealing with large volumes, such as construction, mining, and waste management.

Understanding Cubic Yards

Before diving into cubic yards per hour, let's define the individual unit of cubic yard. A cubic yard is a unit of volume in the imperial and United States customary systems. It is the volume of a cube with sides of one yard (3 feet, 36 inches, or 0.9144 meters) in length.

1 \text{ yd} = 3 \text{ ft} = 36 \text{ in} = 0.9144 \text{ m}

1 \text{ yd}^3 = (1 \text{ yd})^3 = (3 \text{ ft})^3 = 27 \text{ ft}^3

Practical Uses: Landscaping (mulch, soil), concrete, gravel, and waste disposal.

Defining "Per Hour"

"Per hour" simply means "in one hour." This standardizes the rate of flow, allowing for easy comparison and calculation across different scenarios.

How Cubic Yards Per Hour is Formed

Cubic yards per hour combines the unit of volume (cubic yards) with a unit of time (hour) to express flow rate. The formula to calculate volume flow rate ( $Q$ ) is:

Q = \frac{V}{t}