A garden hose with a diameter of 1.7 cm has water flowing in it with a speed of 0.58 m/s. At the end of the hose is a nozzle. If the speed of water in the nozzle is 3.8 m/s, what is the diameter of the nozzle?
as in the previous post,
A*r is constant.
d^2 * 380 = 1.7^2 * 58
thanks. what is the unit
naturally, it's rate of flow: cm^2 * cm/s = cm^3/s
whats d2?
To find the diameter of the nozzle, we need to apply the principle of conservation of mass, which states that the mass flow rate of fluid at one point in a system is equal to the mass flow rate at another point in the same system.
The mass flow rate is given by the equation:
mass flow rate = density * velocity * cross-sectional area
The density of water is a constant, so we can assume it remains constant throughout the hose and nozzle.
Let's assume the cross-sectional area of the hose is A_hose and the cross-sectional area of the nozzle is A_nozzle. We can write the equation for the mass flow rate at the hose as:
mass flow rate_hose = density * velocity_hose * A_hose
Similarly, for the nozzle, we have:
mass flow rate_nozzle = density * velocity_nozzle * A_nozzle
According to the principle of conservation of mass, the mass flow rate at the hose is the same as the mass flow rate at the nozzle:
mass flow rate_hose = mass flow rate_nozzle
density * velocity_hose * A_hose = density * velocity_nozzle * A_nozzle
We can cancel the density from both sides of the equation:
velocity_hose * A_hose = velocity_nozzle * A_nozzle
Now let's substitute the given values into the equation. The velocity of the hose is 0.58 m/s, the diameter of the hose is 1.7 cm, and the velocity of the nozzle is 3.8 m/s. We need to find the diameter of the nozzle, so let's represent it as d_nozzle:
0.58 m/s * π * (1.7 cm/2)^2 = 3.8 m/s * π * (d_nozzle/2)^2
Simplifying the equation further:
0.58 * 0.017^2 = 3.8 * (d_nozzle/2)^2
0.0002651 ≈ (d_nozzle/2)^2
Taking the square root of both sides:
0.01627 ≈ d_nozzle/2
Multiplying both sides by 2 to isolate d_nozzle:
0.03254 ≈ d_nozzle
Therefore, the diameter of the nozzle is approximately 0.03254 meters (or 3.254 cm).