Question

A stiff, 15-cm-long tube with an inner diameter of 2.5 mm is attached to a small hole in the side of a tall beaker. The tube sticks out horizontally. The beaker is filled with 20∘C water to a level 45 cm above the hole, and it is continually topped off to it maintain that level. What is the volume flow rate through the tube?

Answer 1

Volume rate of flow through the pipe is 1.457 × 10⁻⁵ m³/s

Step-by-step explanation:

Given:

Inner diameter of the tube, d = 2.5 mm = 2.5 × 10⁻³ m

water level above the hole, h = 45 cm = 0.45 m

now,

the velocity of the water at the level of hole, v = √(2gh)

thus,

v = √(2 × 9.8 ×.45)

or

v = 2.969 m/s

Now,

the discharge (Q) is given as:

Q = Area × velocity

area of the outlet = πd²/4

or

area = π(2.5 × 10⁻³)²/4 = 4.90 × 10⁻⁶ m²

on substituting the values in the formula for discharge, we get

Q = 4.90 × 10⁻⁶ m² × 2.969 m/s

or

Q = 1.457 × 10⁻⁵ m³/s

hence, the volume rate of flow through the pipe is 1.457 × 10⁻⁵ m³/s