Water (density = 1.00 × 10³ kg/m³)flows at 15.0 m/s through a pipe with radius 0.0400 m.The pipe goes up to the second floor of the building,2.50 m higher,and the pressure remains unchanged.What is the speed of the water flow in the pipe on the second floor? A)13.3 m/s B)16.6 m/s C)176 m/s D)14.2 m/s E)6.63 m/s

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Quizplus · Accepted Answer

To solve this problem, we use the Bernoulli's equation, which in one of its forms can be written as $P_1 + \frac{1}{2}\rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho gh_2$. Given that the pressure remains unchanged and the change in height is 2.5 m, we can simplify the equation to $\frac{1}{2}\rho v_1^2 + \rho gh_1 = \frac{1}{2}\rho v_2^2 + \rho gh_2$. Solving for $v_2$ with the given values ($v_1 = 15.0 m/s$, $h_2 - h_1 = 2.5 m$, $\rho = 1000 kg/m^3$, $g = 9.8 m/s^2$) gives a result of approximately 13.3 m/s.

Water (Density = 1