meters of water @ 4°C to torr conversion

How to convert meters of water @ 4°c to torr?

Certainly! Let's break down how to convert "meters of water at 4°C" to "torr" (mm Hg) step by step, and then look at some real-world examples of other quantities.

Conversion Steps

1. Understand the definition:

   • 1 meter of water column (mH2O) is the pressure exerted by a water column of 1 meter height at 4°C.
   • At 4°C, water has a density (ρ) of approximately 1000 kg/m³.
   • Gravitational acceleration (g) is approximately 9.80665 m/s².

2. Calculate the Pressure in Pascals (Pa): $\text{Pressure (Pa)} = \text{Height (m)} \times \text{Density of water (kg/m³)} \times \text{Gravitational acceleration (m/s²)}$ For 1 mH2O at 4°C: $\text{Pressure} = 1 \, \text{m} \times 1000 \, \text{kg/m³} \times 9.80665 \, \text{m/s²} = 9806.65 \, \text{Pa}$

3. Convert Pascals to Torr: 1 Pascal = 0.00750062 Torr. So, $\text{Pressure (Torr)} = 9806.65 \, \text{Pa} \times 0.00750062 \, \text{Torr/Pa}$ $= 73.5559 \, \text{Torr}$

Therefore, 1 meter of water at 4°C is approximately 73.56 torr.

Real-world Examples

Let's consider other quantities of meters of water:

2 meters of water at 4°C: $2 \, \text{mH2O} \times 9806.65 \, \text{Pa/mH2O} = 19613.3 \, \text{Pa}$ $19613.3 \, \text{Pa} \times 0.00750062 \, \text{Torr/Pa} = 147.112 \, \text{Torr}$

0.5 meters of water at 4°C: $0.5 \, \text{mH2O} \times 9806.65 \, \text{Pa/mH2O} = 4903.325 \, \text{Pa}$ $4903.325 \, \text{Pa} \times 0.00750062 \, \text{Torr/Pa} = 36.778 \, \text{Torr}$

10 meters of water at 4°C: $10 \, \text{mH2O} \times 9806.65 \, \text{Pa/mH2O} = 98066.5 \, \text{Pa}$ $98066.5 \, \text{Pa} \times 0.00750062 \, \text{Torr/Pa} = 735.559 \, \text{Torr}$

In summary:

• 1 mH2O @ 4°C ≈ 73.56 torr
• 2 mH2O @ 4°C ≈ 147.11 torr
• 0.5 mH2O @ 4°C ≈ 36.78 torr
• 10 mH2O @ 4°C ≈ 735.56 torr

These conversions can help you understand the pressure exerted by different heights of water columns in different units.