Water flows straight down from a downspout pipe. The cross-sectional area of the downspout pile is 1.8 m2, and the speed of the water is 0.85 m/s as it leaves the downspout pile. Ignoring air resistance, find the cross-sectional area of the water stream at a point 0.30 m below the faucet.
To find the cross-sectional area of the water stream at a point 0.30 m below the faucet, we can use the principle of conservation of mass. According to this principle, the mass of water entering a certain area must be equal to the mass leaving that area.
Here's how you can solve the problem:
1. First, let's calculate the volume flow rate of water leaving the downspout pipe. The volume flow rate is given by the formula:
Volume flow rate (Q) = Area × Speed
Q = (1.8 m^2) × (0.85 m/s)
Q = 1.53 m^3/s
2. Next, let's assume that the cross-sectional area of the water stream at a point 0.30 m below the faucet is A. Since the water is flowing straight down, the volume flow rate at this point is also equal to Q (1.53 m^3/s).
3. Now, we can use the volume flow rate formula again to find the cross-sectional area (A) at the point 0.30 m below the faucet:
A = Q / Speed
A = 1.53 m^3/s / 0.30 m/s
A ≈ 5.10 m^2
Therefore, the cross-sectional area of the water stream at a point 0.30 m below the faucet is approximately 5.10 m^2.