All Problems

Hydrodynamics

Problem 1.335

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

Reveal Answer
\(1.335 .\) The additional head \(\Delta h=5 \mathrm{~cm}\) at the left-hand end of the tube imparts kinetic energy to the liquid flowing into the tube. From the condition \(\rho v^{2} / 2=\rho g \Delta h\) we get \(v=\sqrt{2 g \Delta h}=1.0 \mathrm{~m} / \mathrm{s}\)