**HP 32S and HP 32SII Week: Jurin's Law - Capillary Rise**

**Capillary Motion**

Jurin's law describes the motion of liquid in small tubes, as the height is inversely proportional to the tube's diameter (and radius). Factors include the contact angle and the density of the liquid.

The height of the liquid is determined by:

h = (2 * σ * cos θ) / (ρ * g * r)

σ = surface tension of the liquid (N/m) (T)

θ = the angle of liquid in degrees, from adhesive (0° to 90°) to cohesive (90° to 180°) (B)

ρ = density of liquid (kg/m^3) (D)

r = radius of the tube (m) (R)

**HP 32S and HP 32SII: Jurin's Law**

Size: 33.5 bytes

J01 LBL J

J02 DEG

J03 INPUT T

J04 INPUT B

J05 INPUT D

J06 INPUT R

J07 2

J08 RCL× T

J09 RCL B

J10 COS

J11 ×

J12 RCL D

J13 RCL× R

J14 9.80665

J15 ×

J16 ÷

J17 STOP

Example:

Find the capillary rise of water in a tube with radius of 0.1 m.

Data: σ = 0.0728 N/m, θ = 0°, and ρ = 1000 kg/m^3

Inputs:

T = 0.0728

B = 0

D = 1000

R = 0.1

Result: 1.48470681E-4 m (height)

Source:

"Jurin's law" Wikipedia. Last updated February 11, 2022. https://en.wikipedia.org/wiki/Jurin%27s_law Last Accessed April 1, 2022.

Lindeburg, Michael R. PE **Civil Engineering Reference Manual for the PE Exam** 14th Edition Professional Publications, Inc: Belmont, CA. pp. 14-11 to 14-13

Eddie

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