Properties of Fluids

N/m

Step 1: Surface tension T is defined as the force per unit length: T = F/L. Step 2: Unit of force = Newton (N), unit of length = metre (m). Step 3: Therefore, unit of surface tension = N/m. Alternatively, surface tension = surface energy per unit area = J/m², which equals N/m. N/m² is the unit of pressure, N·m is the unit of torque/energy. These are common confusions.

4T/r

Step 1: A soap bubble has TWO surfaces — an inner surface and an outer surface, both in contact with air. Step 2: Each surface contributes an excess pressure of 2T/r. Step 3: Total excess pressure = 2T/r + 2T/r = 4T/r. For a liquid drop or air bubble in water (only ONE surface), excess pressure = 2T/r. The factor of 4T/r is specific to soap bubbles because of the two surfaces.

It becomes half

Step 1: The capillary rise formula is h = 2T cosθ / (rρg). Step 2: From the formula, h is inversely proportional to r: h ∝ 1/r. Step 3: If r is doubled (r → 2r), then h → 2T cosθ / (2r × ρg) = (1/2) × original h. So the height becomes half. This explains why water rises much higher in very thin capillaries (like in plant stems) compared to wider ones.

N·s/m²

Step 1: Newton's law of viscosity: F = -η A (dv/dx). Step 2: Rearranging: η = F / [A × (dv/dx)]. Step 3: Units: η = N / (m² × (m/s)/m) = N / (m² × s⁻¹) = N·s/m². This is also written as Pa·s (Pascal-second). The CGS unit is 'poise', where 1 poise = 0.1 N·s/m². N/m² alone is the unit of pressure, not viscosity.