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)
Correct Answer: 0.012
Solution and Explanation
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.
Top IIT JAM GG Geology Questions
- The mineral assemblage found in a granulite facies metabasalt is
- Glossopteris is found in which of the following formations?
- In a sequence of undeformed sedimentary rocks, younger rocks overlie older rocks. This conforms to the principle of
- Dropstones are found in
- The sedimentary structure formed by unidirectional current is
Top IIT JAM GG Applied Geology Questions
- The saturated thickness of an unconfined aquifer is defined by the distance between
- Darcy’s law quantifies the volume of groundwater flow
- The mean flow velocity of water in an open channel having an average depth of 0.2 m, and with Froude Number 4, is ________ m/s. (Round off to one decimal place) (Use $g = 9.8 ms^{-2}$)
- An aquifer has a cross-sectional area of 10 $m^2$ and a hydraulic conductivity of 0.25 cm/s. The volume of water that will flow per second through the aquifer for a hydraulic gradient of 0.04 is _____ $cm^3$. (Round off to three decimal places)
- The geothermal gradient in the continental crust is 0.02 ⁰C/m. If the surface temperature is 25 ⁰C, the temperature at a depth of 18 km from the surface is ________ ⁰C. (In integer)
Top IIT JAM GG Questions
- The mineral assemblage found in a granulite facies metabasalt is
- Glossopteris is found in which of the following formations?
- In a sequence of undeformed sedimentary rocks, younger rocks overlie older rocks. This conforms to the principle of
- Dropstones are found in
- The sedimentary structure formed by unidirectional current is