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Hydrodynamics

Problem 1.335

In the arrangement shown in Fig. 1.90 a viscous liquid whose density is ρ=1.0 g/cm3\rho=1.0 \mathrm{~g} / \mathrm{cm}^{3} flows along a tube out of a wide tank AA. Find the velocity of the liquid flow, if h1=10 cm,h2=20 cm,h_{1}=10 \mathrm{~cm}, h_{2}=20 \mathrm{~cm}, and h3=35 cm.h_{3}=35 \mathrm{~cm} . All the distances ll are equal.

Reveal Answer
1.335.1.335 . The additional head Δh=5 cm\Delta h=5 \mathrm{~cm} at the left-hand end of the tube imparts kinetic energy to the liquid flowing into the tube. From the condition ρv2/2=ρgΔh\rho v^{2} / 2=\rho g \Delta h we get v=2gΔh=1.0 m/sv=\sqrt{2 g \Delta h}=1.0 \mathrm{~m} / \mathrm{s}
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