an ideal fluid in a pipe of diameter 14cm is moving at 6.0m/s. If the incompressible fluid density is 1.05grams/cc, what is the flow rate in kg/s and what is the speed of flow if the pipe narrows to 4.0cm radius?
what was the answer
To determine the flow rate in kg/s, we need to use the formula:
Flow rate (Q) = Area (A) * Velocity (v) * Density (ρ)
First, let's calculate the current flow rate using the given diameter of 14cm.
1. Find the radius of the pipe:
Radius (r) = Diameter (d) / 2
r = 14cm / 2
r = 7cm = 0.07m
2. Calculate the area of the pipe:
Area (A) = π * r^2
A = π * (0.07m)^2
3. Plug in the given values:
Flow rate (Q) = A * v * ρ
Q = π * (0.07m)^2 * 6.0m/s * 1.05g/cc
Now, let's convert the flow rate from g/cc to kg/s:
1. Convert density from grams/cc to kg/m^3:
ρ = 1.05g/cc * 1000 kg/g
ρ = 1050 kg/m^3
2. Convert flow rate units from m^3/s to kg/s:
Flow rate (Q) = Q * A * v * ρ
Q = π * (0.07m)^2 * 6.0m/s * 1050 kg/m^3
Next, let's calculate the speed of flow if the pipe narrows to a 4.0cm radius.
1. Find the radius of the narrowed pipe:
r = 4.0cm / 2 = 0.04m
2. Calculate the area of the narrowed pipe:
A = π * r^2
A = π * (0.04m)^2
3. Plug in the given values:
Flow rate (Q) = A * v * ρ
Q = π * (0.04m)^2 * v * 1050 kg/m^3
Now, we have equations for the flow rate in both cases. To solve for the unknown values, we need more information, such as the new speed of flow (v) when the pipe narrows.