You are stranded on a barren island without any electronic or mechanical items a

Question

You are stranded on a barren island without any electronic or mechanical items available to you. However, the native tigers are big fans of Physical Oceanographers and promise not to eat you if you can determine how fast the water in the local river is flowing (i.e. either the velocity or the volume flow rate). The river is 7 m wide, 1 km long, and has an average uniform depth of 10 m. Describe a method that you could use to find this information. (remember: no modern measuring devices are allowed, but anything else is free game). Can your method determine if water at different spots (horizontally or vertically) in the river is moving at different velocities ? (that is, whether or not the velocity profile is uniform.)

Explanation / Answer

Answer: The velocity of water in the local river can be measured easily by the float method wherein one simply measures the time it takes for a floating object (e.g., a piece of wood, a fruit peel, a flower or leaf, etc.) to travel a measured distance. By this method velocity at different regions and points in the river can also be measured by dividing the length of the river (1 Km) into smaller sections. Here time can be measured from a watch or from the pulse (in the absence of a watch).

The volume flow rate can also be measured, without using the modern measuring devices, at any point in the river by using the given data of the depth (stage height) and width of the river, by using the formula

Cross sectional area at a certain point × velocity at that point

where cross sectional area = width × stage height

or Q =AV

Q = discharge/volume flow rate (volume per unit time)

A = cross sectional area of the river

V = velocity of the river at any point

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