The Honey Drizzle Timer · AI Generator #GEN-583121CD

Physics · fluid-mechanics

Problem

A chef notices that honey drizzles from a spoon in a remarkably steady stream, and decides to use this as a kitchen timer. When honey (density

\rho = 1400\;\text{kg/m}^3

, viscosity

\eta = 10\;\text{Pa·s}

) flows through a thin cylindrical channel of length

L = 2.0\;\text{cm}

and radius

r = 0.50\;\text{mm}

under a pressure difference created by the weight of honey in a small reservoir above, the flow rate is

Q = 8.0 \times 10^{-9}\;\text{m}^3\text{/s}

. What is the effective height

h

of the honey column above the channel that creates this flow rate? Assume the flow is laminar and use

g = 10\;\text{m/s}^2