FIGURE 15-11
-Water flows in the horizontal pipe shown in Figure 15-11. At A the diameter is 6.00 cm and at B the diameter is 5.00 cm. The fluid in the manometer is oil, which has a density of 800 kg/m³. The manometer reading h is 9.00 cm. What volume of water is flowing through the pipe per second?

Question

FIGURE 15-11

-Water flows in the horizontal pipe shown in Figure 15-11. At A the diameter is 6.00 cm and at B the diameter is 5.00 cm. The fluid in the manometer is oil, which has a density of 800 kg/m³. The manometer reading h is 9.00 cm. What volume of water is flowing through the pipe per second?

Quizplus · Accepted Answer

The correct answer is A.The volume of water flowing through the pipe per second is given by:$$Q = Av$$where:* Q is the volume flow rate (m^3/s)* A is the cross-sectional area of the pipe (m^2)* v is the velocity of the water (m/s)The cross-sectional area of the pipe is given by:$$A = \pi r^2$$where:* r is the radius of the pipe (m)The velocity of the water is given by:$$v = \frac{Q}{A}$$Substituting the expressions for A and v into the equation for Q, we get:$$Q = \frac{\pi r^2 Q}{\pi r^2}$$$$Q = Q$$Therefore, the volume of water flowing through the pipe per second is equal to the volume flow rate.The volume flow rate can be calculated using the Bernoulli equation:$$P_1 + \frac{1}{2} ho v_1^2 + ho g y_1 = P_2 + \frac{1}{2} ho v_2^2 + ho g y_2$$where:* P is the pressure (Pa)* ρ is the density of the fluid (kg/m^3)* v is the velocity of the fluid (m/s)* g is the acceleration due to gravity (m/s^2)* y is the height of the fluid (m)Assuming that the pressure at points A and B is the same, and that the velocity of the water at point A is negligible, we can simplify the Bernoulli equation to:$$\frac{1}{2} ho v_2^2 = ho g h$$Solving for v2, we get:$$v_2 = \sqrt{2gh}$$Substituting the expression for v2 into the equation for Q, we get:$$Q = \pi r^2 \sqrt{2gh}$$Substituting the given values into the equation, we get:$$Q = \pi (0.0250 	ext{ m})^2 \sqrt{2(9.81 	ext{ m/s}^2)(0.0900 	ext{ m})}$$$$Q = 0.00324 	ext{ m}^3/	ext{s}$$Therefore, the volume of water flowing through the pipe per second is 0.00324 m^3/s.

FIGURE 15-11 -Water Flows in the Horizontal Pipe Shown in Figure 15-11