Physics of Low Pressure Systems

This solution details the calculation for centrifugal force per unit mass acting on air within a low-pressure centre.

Centrifugal Force Calculation

Centrifugal force per unit mass is equivalent to centrifugal acceleration ($a_c$). This outward force arises from the inertia of the air moving along a curved path around the low-pressure centre.

Formula Applied

The formula for centrifugal acceleration is:

$a_c = \frac{v^2}{r}$

Where:

• $v$ represents the wind speed.
• $r$ represents the distance from the low-pressure centre.

Calculation Steps

1. Given Information:

   Wind speed, $v = 10 \text{ m.s}^{-1}$.

   Distance from centre, $r = 250 \text{ km}$.

2. Unit Conversion:

   Convert the distance $r$ to meters for consistency:

   $r = 250 \text{ km} \times 1000 \text{ m/km} = 250,000 \text{ m} = 2.5 \times 10^5 \text{ m}$.

3. Magnitude Calculation:

   Substitute the values into the formula:

   $a_c = \frac{(10 \text{ m.s}^{-1})^2}{2.5 \times 10^5 \text{ m}} = \frac{100 \text{ m}^2\text{s}^{-2}}{2.5 \times 10^5 \text{ m}}$

   $a_c = \frac{1 \times 10^2}{2.5 \times 10^5} \text{ m.s}^{-2} = 0.4 \times 10^{-3} \text{ m.s}^{-2}$

   $a_c = 4 \times 10^{-4} \text{ m.s}^{-2}$

4. Sign Convention:

   In atmospheric dynamics concerning low-pressure systems, forces directed towards the centre (like the pressure gradient force) are often considered positive. Since centrifugal force acts outwards, it is conventionally represented with a negative sign in this context.

   Therefore, the centrifugal force per unit mass is $-4 \times 10^{-4} \text{ m.s}^{-2}$.