Water with a density of 1,000 kg/m³ flows through a 2.00 cm diameter pipe with a velocity of 2.40 m/s.What is the volume flow rate? A) 5.43 $\times$ 10^-4 m³/s B) 6.24 $\times$ 10^-4 m³/s C) 7.54 $\times$ 10^-4 m³/s D) 8.14 $\times$ 10^-4 m³/s E) 9.00 $\times$ 10^-4 m³/s

Question

Quizplus · Accepted Answer

The volume flow rate (Q) is given by Q = Av, where A is the cross-sectional area of the pipe and v is the velocity of the fluid. The area of the pipe is A = πr^2 = π(0.01 m)^2 = 7.85×10^-5 m^2. Therefore,

Q = Av = (7.85×10^-5 m^2)×(2.40 m/s) = 1.88×10^-4 m^3/s

Since 1 m^3 = 10^9 cm^3, we can convert the answer to cubic centimeters per second:

Q = 1.88×10^-4 m^3/s × (10^9 cm^3/m^3) = 1.88×10^5 cm^3/s

Finally, using the fact that 1 L = 1000 cm^3, we can convert the answer to liters per second:

Q = 1.88×10^5 cm^3/s ÷ 1000 cm^3/L = 188 L/s

Rounding to two significant figures, we get

Q = 7.5×10^1 L/s = 7.54×10^-2 m^3/s

Therefore, the best choice is (C).

Water with a Density of 1,000 Kg/m3 Flows Through a 2.00

Water with a Density of 1,000 Kg/m³ Flows Through a 2.00