Water flows through a 1.2 cm diameter pipe into a 155 L bathtub, which it fills in 8 min.What is the speed of the water in the pipe?
To find the speed of the water in the pipe, we need to calculate the volume flow rate. Volume flow rate is defined as the volume of fluid passing through a given cross-sectional area per unit of time.
First, we need to calculate the cross-sectional area of the pipe. The diameter of the pipe is given as 1.2 cm, so we can use the formula for the area of a circle: A = πr^2, where r is the radius of the pipe. The radius is half the diameter, so it would be 0.6 cm or 0.006 m (since 1 cm = 0.01 m).
A = π * (0.006 m)^2
A = 0.000113 m^2
Next, we calculate the volume flow rate. We know that 155 L of water fills the bathtub in 8 min, and we want to find the flow in m^3/s. We'll convert the volume and time to m^3 and seconds respectively.
Volume_flow_rate = Volume / Time
Volume = 155 L = 0.155 m^3 (since 1 L = 0.001 m^3)
Time = 8 min = 480 s (since 1 min = 60 s)
Volume_flow_rate = 0.155 m^3 / 480 s
Volume_flow_rate = 0.000323 m^3/s
Finally, we can calculate the speed of the water in the pipe using the volume flow rate and the cross-sectional area.
Speed = Volume_flow_rate / Cross-sectional area
Speed = 0.000323 m^3/s / 0.000113 m^2
Speed ≈ 2.858 m/s (rounded to three decimal places)
Therefore, the speed of the water in the pipe is approximately 2.858 m/s.