Question

During typical urination, a man releases about 400 mL of urine in about 30 seconds through the urethra, which we can model as a tube 4 mm in diameter and 20 cm long. Assume that urine has the same density as water, and that viscosity can be ignored for this flow. a. What is the flow speed in the urethra

Answer 1

Answer:

The flow speed in the urethra is 3.77 m/s

Explanation:

The flow rate or speed of a liquid is a measure of the volume of liquid that flows in a given amount of time.

Fluid flow rate, Q = area of the pipe or channel × velocity of the liquid

Q = A × v ; where Q is  in m³/s or L/s; A is in m²; velocity, v = is in m/s

Also flow rate, Q = volume/time

volume, V, is in m³ and time is in seconds

therefore, V/t = A × v

v = At / V

Volume, V = 400 mL = 0.4 L = 4 × 10⁻⁴ m³

Area, A, of tube = πr², where r is radius in meters

r = 4 mm = 4 × 10⁻³ m

A = 22/7 × (4 × 10⁻³ m)²

therefore, v = {22/7 × (4 × 10⁻³ m)² × 30}/4 × 10⁻⁴ m³

v = 3.77 m/s

Therefore, the flow speed in the urethra is 3.77 m/s