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  4. Water is flowing at a speed of 1.5 ms-1 through a horizontal tube of cross-sectional area 10-2m2 and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water = 103 kgm-3).

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Q. Water is flowing at a speed of $1.5\, ms^{-1}$ through a horizontal tube of cross-sectional area $10^{-2}m^2$ and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water = $10^3\, kgm^{-3}$).

JEE MainJEE Main 2014Mechanical Properties of Fluids

Solution:

$F=v \frac{dm}{dt}$
$=v\,Apv$
$=v^{2}Apv$
$=\left(1.5\right)^{2}\times10^{-2}\times 10^{3}$
$=2.25\times 10=22.5\,N$