Air at 70 F flows in a .8 inch diameter horizontal pipe. The density of the air is constant at .077 lbm/ft3. Assuming fully-developed flow determine the maximum pressure drop over a 30 ft section of pipe if the flow is laminar.
Ans. = .00288psi
To determine the maximum pressure drop over a 30 ft section of pipe, we need to calculate the pressure drop due to friction in laminar flow.
First, let's calculate the Reynolds number (Re) to determine if the flow is laminar or turbulent. The Reynolds number can be calculated using the formula:
Re = (density × velocity × diameter) / viscosity
Where:
- density is the density of air (given as 0.077 lbm/ft^3)
- velocity is the flow velocity
- diameter is the diameter of the pipe (given as 0.8 inch, which can be converted to feet by dividing by 12)
- viscosity for air can be approximated as 3.5 × 10^(-7) lbm/(ft·s)
Now, let's plug in the values and calculate the Reynolds number:
Re = (0.077 lbm/ft^3 × velocity × (0.8 inch / 12 ft/inch)) / (3.5 × 10^(-7) lbm/(ft·s))
Since we are assuming fully-developed flow, the flow velocity will be constant across the entire section of pipe. Since we do not have the actual flow velocity, we cannot calculate the Reynolds number. However, we are given that the flow is laminar, so we can proceed with the assumption that the flow is indeed laminar.
In laminar flow, the pressure drop due to friction (ΔP) can be calculated using the following equation:
ΔP = (32 × viscosity × length × velocity) / (diameter^2)
Where:
- viscosity is the viscosity of air (given as 3.5 × 10^(-7) lbm/(ft·s))
- length is the length of the pipe section (given as 30 ft)
- velocity is the flow velocity
- diameter is the diameter of the pipe (given as 0.8 inch, which can be converted to feet by dividing by 12)
Now, let's plug in the values and calculate the pressure drop:
ΔP = (32 × (3.5 × 10^(-7) lbm/(ft·s)) × 30 ft × velocity) / ((0.8 inch / 12 ft/inch)^2)
Simplifying the equation:
ΔP = (32 × 3.5 × 10^(-7) × 30 × velocity) / (0.006667^2) psi
ΔP = (1.344 × 10^(-5) × velocity) psi
Given that the pressure drop (ΔP) is 0.00288 psi, we can solve for the flow velocity:
0.00288 psi = (1.344 × 10^(-5) × velocity) psi
velocity = 0.00288 psi / (1.344 × 10^(-5)) psi
velocity ≈ 214.29 ft/s
Therefore, the flow velocity is approximately 214.29 ft/s in order to have a pressure drop of 0.00288 psi over a 30 ft section of pipe.