Pints per second (pnt/s) to Imperial Gallons per Hour (imp-gal/h) conversion

What is the pint per second?

Pints per second (pint/s) measures the volume of fluid that passes a point in a given amount of time. It's a unit of volumetric flow rate, commonly used for liquids.

Understanding Pints per Second

Pints per second is a rate, indicating how many pints of a substance flow past a specific point every second. It is typically a more practical unit for measuring smaller flow rates, while larger flow rates might be expressed in gallons per minute or liters per second.

Formation of the Unit

The unit is derived from two base units:

• Pint (pint): A unit of volume. In the US system, there are both liquid and dry pints. Here, we refer to liquid pints.
• Second (s): A unit of time.

Combining these, we get pints per second (pint/s), representing volume per unit time.

Formula and Calculation

Flow rate ($Q$) is generally calculated as:

$Q = \frac{V}{t}$

Where:

• $Q$ is the flow rate (in pints per second)
• $V$ is the volume (in pints)
• $t$ is the time (in seconds)

Real-World Examples & Conversions

While "pints per second" might not be the most common unit encountered daily, understanding the concept of volume flow rate is crucial. Here are a few related examples and conversions to provide perspective:

• Dosing Pumps: Small dosing pumps used in chemical processing or water treatment might operate at flow rates measurable in pints per second.
• Small Streams/Waterfalls: The flow rate of a small stream or the outflow of a small waterfall could be estimated in pints per second.

Conversions to other common units:

• 1 pint/s = 0.125 gallons/s
• 1 pint/s = 7.48 gallons/minute
• 1 pint/s = 0.473 liters/s
• 1 pint/s = 473.176 milliliters/s

Related Concepts and Applications

While there isn't a specific "law" tied directly to pints per second, it's essential to understand how flow rate relates to other physical principles:

• Fluid Dynamics: Pints per second is a practical unit within fluid dynamics, helping to describe the motion of liquids.

• Continuity Equation: The principle of mass conservation in fluid dynamics leads to the continuity equation, which states that for an incompressible fluid in a closed system, the mass flow rate is constant. For a fluid with constant density $\rho$, the volumetric flow rate $Q$ is constant. Mathematically, this can be expressed as:

  $A_1v_1 = A_2v_2$

  Where $A$ is the cross-sectional area of the flow and $v$ is the average velocity. This equation means that if you decrease the cross-sectional area, the velocity of the flow must increase to maintain a constant flow rate in $m^3/s$ or $pint/s$.

• Hagen-Poiseuille Equation: This equation describes the pressure drop of an incompressible and Newtonian fluid in laminar flow through a long cylindrical pipe. Flow rate is directly proportional to the pressure difference and inversely proportional to the fluid's viscosity and the length of the pipe.

  $Q = \frac{\pi r^4 \Delta P}{8 \eta L}$

  Where:

  • $Q$ is the volumetric flow rate (e.g., in $m^3/s$).
  • $r$ is the radius of the pipe.
  • $\Delta P$ is the pressure difference between the ends of the pipe.
  • $\eta$ is the dynamic viscosity of the fluid.
  • $L$ is the length of the pipe.

What is the Imperial Gallon per Hour?

The imperial gallon per hour (imp-gal/h) is a unit of volumetric flow rate expressing how many imperial gallons of fluid pass a point in one hour. It is used in the UK and other Commonwealth countries for pumps, fuel consumption, and plumbing flow ratings.

Definition

One imperial gallon per hour equals one imperial gallon of volume divided by one hour (3,600 seconds):

$$1\ \text{imp-gal/h} = 0.00126280\ \text{l/s}$$

The imperial gallon is defined as exactly 4.54609 litres, so dividing by 3,600 seconds gives 4.54609 / 3600 = 0.00126280 L/s (equivalently 4.54609 L/h).

Origin and History

The imperial gallon was established by the British Weights and Measures Act of 1824, originally defined as the volume of 10 pounds of water at a specified temperature. It was later fixed by reference to the litre. The "per hour" rate arose naturally in the 19th and 20th centuries as a practical measure for pump throughput and fuel usage, hours being a convenient interval for slow, steady flows.

Law and Notable Facts

The imperial gallon (4.54609 L exactly) is legally distinct from and about 20% larger than the US liquid gallon of 3.785411784 L. As a result an imperial gallon per hour is likewise about 20% greater than a US gallon per hour. Since UK metrication, the imperial gallon is no longer a primary trade unit but persists in fuel-economy figures (miles per gallon) and equipment specifications.

Real-World Examples and Conversions

• A small garden or aquarium pump rated at 100 imp-gal/h moves about 454.6 litres of water every hour, roughly 0.126 L/s.
• A domestic tap running at 1 imperial gallon per hour is a bare trickle of about 4.55 L each hour.
• 1 imp-gal/h ≈ 0.833 US gal/h, reflecting the larger imperial gallon.
• A pump moving 220 imp-gal/h delivers about 1,000 L/h, or roughly 0.278 L/s.