Question

A cylindrical soil sample is encased in an open-ended inclined tube with a diameter of 100 mm. There is a constant supply of water from the upper end of the sample and the outflow from the other end is collected in a beaker. The average amount of water collected is 1000 mm³ every 10 sec. The average outflow velocity is ________mm/sec. (π = 3.14) (Round off to three decimal places)

Answer 1

Correct Answer: 0.012

To determine the average outflow velocity of water from the cylindrical soil sample, we can use the formula for velocity, v, which is given by:
v = Q/A
where Q is the volumetric flow rate and A is the cross-sectional area of the tube.
First, calculate the cross-sectional area, A, of the tube. The formula for the area of a circle is:
A = π(d/2)², where d is the diameter of the tube.
Here, d = 100 mm.
Thus, A = 3.14 × (100/2)² = 3.14 × 50² = 3.14 × 2500 = 7850 mm².
Now, calculate the volumetric flow rate, Q. Given that 1000 mm³ of water is collected every 10 seconds, Q = 1000 mm³ per 10 sec = 100 mm³/sec.
Substitute Q and A into the velocity formula:
v = 100/7850
v ≈ 0.012738.
Rounded to three decimal places, the average outflow velocity is approximately 0.013 mm/sec.