Water flowing through 1.9 cm-diameter pipe can fill 480 L bathtub in 301 s. What is the speed of the water in the pipe? [1𝐿=10−3𝑚3]

Sure, let's solve this step by step:

Step 1: Convert the volume of the bathtub from liters to cubic meters. Given that 1 L = 10^-3 m^3, we have 480 L = 480 * 10^-3 m^3 = 0.48 m^3.

Step 2: Calculate the flow rate, which is the volume of water that flows per unit of time. Flow rate = Volume / Time = 0.48 m^3 / 301 s = 0.001594682 m^3/s.

Step 3: Calculate the cross-sectional area of the pipe. The diameter of the pipe is given as 1.9 cm, so the radius is 1.9 cm / 2 = 0.95 cm = 0.0095 m. The cross-sectional area A of the pipe is given by the formula A = πr^2, where r is the radius of the pipe. So, A = π * (0.0095 m)^2 = 0.000283 m^2.

Step 4: Calculate the speed of the water. The speed v of the water is given by the formula v = Flow rate / Area. So, v = 0.001594682 m^3/s / 0.000283 m^2 = 5.63 m/s.

Therefore, the speed of the water in the pipe is 5.63 m/s.