Question

a pipe of radius 0.0100 m carries water at 2.33 m/s. how much time does it take to fill up a 1.00 m³ fish tank? ? s

Explanation:

Step1: Calculate the cross - sectional area of the pipe

The pipe is circular, and the formula for the area of a circle is $A=\pi r^{2}$. Given that $r = 0.0100\ m$, we substitute this value into the formula:
$A=\pi\times(0.0100)^{2}=\pi\times1\times 10^{- 4}\ m^{2}\approx3.1416\times10^{-4}\ m^{2}$

Step2: Calculate the volume flow rate ($Q$) of water

The volume flow rate is given by the product of the cross - sectional area ($A$) and the velocity ($v$) of the fluid, i.e., $Q = A\times v$. We know that $A\approx3.1416\times10^{-4}\ m^{2}$ and $v = 2.33\ m/s$. So,
$Q=3.1416\times 10^{-4}\ m^{2}\times2.33\ m/s\approx7.32\times 10^{-4}\ m^{3}/s$

Step3: Calculate the time ($t$) to fill the tank

The volume of the tank is $V = 1.00\ m^{3}$. The formula that relates volume, flow rate, and time is $V=Q\times t$, so we can solve for $t$ as $t=\frac{V}{Q}$. Substituting $V = 1.00\ m^{3}$ and $Q\approx7.32\times 10^{-4}\ m^{3}/s$:
$t=\frac{1.00}{7.32\times 10^{-4}}\ s\approx1366\ s$

Answer:

$\approx1366$