Water is flowing through a pipe (area 4.0 cm2) that connects to a faucet adjusted to have an opening of 0.57 cm2. If the water is flowing at a speed of 5.3 m/s in the pipe, how long does it take for water from the faucet to fill a bucket of volume 0.11 m3?
Q = volume flow rate
= (pipe area) * 5.3 m/s
= 2.12*10^-3 m^3/s
Let time required = T
Q*T = 0.11 m^3
T = 52 s
To find out how long it takes for water from the faucet to fill a bucket of volume 0.11 m3, we can use the concept of volumetric flow rate.
The volumetric flow rate can be calculated by multiplying the cross-sectional area of the pipe by the velocity of the water flow. In this case, the area of the pipe is 4.0 cm2 (or 4.0 x 10^-4 m2), and the velocity of the water flow is 5.3 m/s.
Volumetric flow rate (Q) = Area x Velocity
So, Q = 4.0 x 10^-4 m2 x 5.3 m/s
Next, we need to calculate the time taken to fill the bucket. We know that the volume of the bucket is 0.11 m3.
Time (t) = Volume / Volumetric flow rate
Substituting the values, t = 0.11 m3 / (4.0 x 10^-4 m2 x 5.3 m/s)
Simplifying the equation further, t = 0.11 / (4.0 x 10^-4 x 5.3) sec
So, to calculate the time, divide 0.11 by the product of (4.0 x 10^-4) and 5.3.