L Hr To Cm Hr

Understanding the Conversion: L hr to cm hr

When you see the unit L hr (liters per hour) you are looking at a volume‑flow rate. The unit cm hr (centimeters per hour) represents a linear speed. Converting directly from L hr to cm hr is not a simple arithmetic operation; it requires additional information about the cross‑sectional area through which the fluid moves. This article explains the theory behind the conversion, the necessary data, and step‑by‑step calculations you can apply in physics, engineering, or quantitative aptitude problems.

Why a Direct Conversion Is Impossible

Volume and length are different physical dimensions:

• L hr – volume (L) divided by time (hr).
• cm hr – distance (cm) divided by time (hr).

To link them you must know the area (A) through which the fluid travels. The relationship is derived from the basic definition of flow rate:

Q = A × v

where Q is the volumetric flow (L hr), A is the cross‑sectional area (cm²), and v is the linear speed (cm hr). Rearranging gives the conversion formula:

v (cm hr) = Q (L hr) × 1000 cm³/L ÷ A (cm²)

Thus, the conversion hinges on the area of the pipe, channel, or any conduit carrying the fluid.

Step‑by‑Step Conversion Procedure

1. Obtain the volumetric flow rate (Q). This value is usually given in liters per hour.
2. Determine the cross‑sectional area (A). For a circular pipe, use the diameter (d) in centimeters:
   • A = π × (d/2)²
   For a rectangular channel, multiply width by height (both in centimeters).
3. Convert Q to cubic centimeters per hour. Multiply by 1,000 because 1 L = 1,000 cm³.
4. Apply the conversion formula. Divide the cubic centimeters per hour by the area (cm²) to obtain cm hr.
5. Check units. The result should be expressed in centimeters per hour, confirming that the dimensions cancel correctly.

Practical Example: Pipe Flow

Suppose a water pump delivers 150 L hr⁻¹ through a pipe with an internal diameter of 5 cm**.**