Answer to Question #169399 in Physics for Nicole

Question

1) An ideal fluid is flowing at a rate of 1.8m³/s through a pipe with a radius of 2.0 cm (a) What is the speed of the fluid through the pipe? suppose that in one portion, the pipe is clogged, and the radius decreased to 1.7cm. What are the (b) volumetric flow rate and (c) speed through the clogged portion?

2) A dam holds back the water in a lake. If the dam has a small hole, 1.4 meters below the surface of the lake, then at what speed does water exit the hole?

Answer 1

1) a)

$$1.8=\pi(0.02)^2v\\v=1432\frac{m}{s}$$

b)

$$C=\frac{m^3}{s}$$

c)

$$1.8=\pi(0.017)^2u\\u=1983\frac{m}{s}$$

2)

$$v=\sqrt{2gh}\\v=\sqrt{2(9.8)(1.4)}=5.2\frac{m}{s}$$