Water flows in the horizontal pipe shown in the figure.At point A the area is 25.0 cm² and the speed of the water is At B the area is 16.0 cm².The fluid in the manometer is mercury,which has a density of 13,600 kg/m³.We can treat water as an ideal fluid having a density of 1000 kg/m³.What is the manometer reading h? A) 0.546 cm B) 1.31 cm C) 2.81 cm D) 2.16 cm E) 3.36 cm

Question

Quizplus · Accepted Answer

From the Bernoulli's equation, we have:
$P_A + \frac{1}{2}ho v_A^2 + ho g h = P_B + \frac{1}{2}ho v_B^2$
We can assume that the pressure at A and B are the same (since the pipe is horizontal). Also, $v_B = 0$ since the pipe widens and the water slows down. Therefore:
$\frac{1}{2}ho v_A^2 = ho g h$
$h = \frac{1}{2g}ho v_A^2$
$h = \frac{1}{2g}ho A_A^{-2}v_A^2$
$h = \frac{1}{2g}\frac{ho}{A_A^{-2}}v_A^2$
$h = \frac{1}{2g}\frac{1000}{0.25^{-2}}(0.11)^2$
$h \approx 0.0216 	ext{ m} = \boxed{2.16 	ext{ cm}}$

Water Flows in the Horizontal Pipe Shown in the Figure