Question

suppose pure water flows through a tube of diameter 0.00300 m, at a speed of 0.800 m/s. what is the volume flow rate through the tube? ? × 10^? m³/s

Explanation:

Step1: Find the radius of the tube

The diameter \( d = 0.00300 \, \text{m} \), so the radius \( r=\frac{d}{2}=\frac{0.00300}{2}=0.00150 \, \text{m} \)

Step2: Calculate the cross - sectional area of the tube

The formula for the area of a circle is \( A = \pi r^{2} \). Substituting \( r = 0.00150 \, \text{m} \), we get \( A=\pi\times(0.00150)^{2}=\pi\times2.25\times 10^{- 6}\approx7.0686\times10^{-6}\, \text{m}^2 \)

Step3: Calculate the volume flow rate

The volume flow rate \( Q \) is given by the formula \( Q=A\times v \), where \( v = 0.800 \, \text{m/s} \) is the speed of the fluid. Substituting \( A\approx7.0686\times 10^{-6}\, \text{m}^2 \) and \( v = 0.800 \, \text{m/s} \), we have \( Q=7.0686\times 10^{-6}\times0.800 = 5.6549\times10^{-6}\, \text{m}^3/\text{s} \)

Answer:

\( 5.65 \times 10^{-6} \) (or more precisely \( 5.6549\times10^{-6} \))