a tube of 1mm bore is dipped into a vessel containing a liquid of density 0.8g/cm³,surface tension 30dyne/cm and angle of contact 0. calculate the length which the liquid will occupy in the tube when the tube is held (b) inclined to the vertical at an angle of 30

To determine how high the liquid will rise in a tube with a 1mm bore when it's inclined at an angle of 30 degrees, we can apply the principles of capillarity. This phenomenon occurs due to the interplay of surface tension, liquid density, and the geometry of the tube. Let’s break down the calculations step by step.

Understanding Capillarity

Capillary action refers to the ability of a liquid to flow in narrow spaces without the assistance of external forces. In this case, the height to which the liquid rises in the tube can be calculated using the formula:

Capillary Rise Formula

The height of the liquid column (h) in a capillary tube can be determined using the formula:

h = (2 * γ * cos(θ)) / (ρ * g * r)

• h: height of the liquid column
• γ: surface tension of the liquid (in dynes/cm)
• θ: angle of contact
• ρ: density of the liquid (in g/cm³)
• g: acceleration due to gravity (approximately 980 cm/s²)
• r: radius of the tube (in cm)

Parameters for Calculation

Let's plug in the values provided in your question:

• Surface tension (γ) = 30 dyne/cm
• Density (ρ) = 0.8 g/cm³
• Radius of the tube (r) = 0.05 cm (since the bore is 1mm, the radius is half of that)
• Angle of contact (θ) = 0 degrees (as it is not specified that it is inclined initially, we will first calculate it for vertical)

Calculating Height when Vertical

When the tube is vertical (θ = 0 degrees), cos(0) = 1. Plugging these values into the formula:

h = (2 * 30 * 1) / (0.8 * 980 * 0.05)

Calculating this gives:

h = 60 / (39.2) ≈ 1.53 cm

Calculating Height when Inclined

Now, when the tube is inclined at an angle of 30 degrees, we need to consider the cosine of 30 degrees, which is approximately 0.866. Now let's recalculate:

h = (2 * 30 * cos(30°)) / (0.8 * 980 * 0.05)

Substituting the values:

h = (2 * 30 * 0.866) / (0.8 * 980 * 0.05)

This simplifies to:

h = (51.96) / (39.2) ≈ 1.32 cm

Final Results

Thus, when the tube is vertical, the liquid will rise approximately 1.53 cm. When the tube is inclined at 30 degrees, the liquid will rise approximately 1.32 cm. This demonstrates how the angle of inclination affects the height of the liquid column in a capillary tube, showcasing the principles of fluid dynamics and surface tension at play.