Cubic yards per second to Cubic inches per hour conversion

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

To convert from cubic yards per second (yd³/s) to cubic inches per hour (in³/hr), you need to follow a series of unit conversions.

1 cubic yard (yd³) is equivalent to 46,656 cubic inches (in³): $1 \text{ yd}^3 = 27 \text{ ft}^3$ $1 \text{ ft}^3 = 1,728 \text{ in}^3$ Multiplying these: $1 \text{ yd}^3 = 27 \times 1,728 \text{ in}^3 = 46,656 \text{ in}^3$

There are 3,600 seconds in an hour: $1 \text{ hour} = 3,600 \text{ seconds}$

Using these conversions, let's carry out the conversions step-by-step:

Step-by-Step Conversion:

1. Convert cubic yards to cubic inches: $1 \text{ yd}^3/\text{sec} = 46,656 \text{ in}^3/\text{sec}$

2. Convert seconds to hours: $1 \text{ yd}^3/\text{sec} = 46,656 \text{ in}^3/\text{sec} \times 3,600 \text{ sec/hr}$

3. Multiply: $46,656 \text{ in}^3/\text{sec} \times 3,600 \text{ sec/hr} = 167,961,600 \text{ in}^3/\text{hr}$

So, 1 cubic yard per second (yd³/s) is equal to 167,961,600 cubic inches per hour (in³/hr).

Real-World Examples of Other Quantities:

1. 1.5 yd³/s: $1.5 \text{ yd}^3/\text{sec} \times 167,961,600 \text{ in}^3/\text{hr} = 251,942,400 \text{ in}^3/\text{hr}$ This flow rate could represent a large industrial water discharge or a significant river flow.

2. 0.5 yd³/s: $0.5 \text{ yd}^3/\text{sec} \times 167,961,600 \text{ in}^3/\text{hr} = 83,980,800 \text{ in}^3/\text{hr}$ This could approximate the flow rate in a medium-sized water distribution system or a fast-moving creek.

3. 2 yd³/s: $2 \text{ yd}^3/\text{sec} \times 167,961,600 \text{ in}^3/\text{hr} = 335,923,200 \text{ in}^3/\text{hr}$ This might represent the outflow of a large hydroelectric dam when releasing water downstream.

4. 0.1 yd³/s: $0.1 \text{ yd}^3/\text{sec} \times 167,961,600 \text{ in}^3/\text{hr} = 16,796,160 \text{ in}^3/\text{hr}$ Such a rate might be seen in a small-scale irrigation system or moderate water flow from a hillside spring.

These examples help give context to the flow rates in various applications ranging from natural water bodies to engineered water distribution systems.