Sample Problems and Solutions
When given a pump with the following characteristics:
- Impeller diameter (D₁) = 6 in
- Total head (H₁) = 100 ft
- Flow rate (Q₁) = 100 gpm
- Speed (N₁) = 1800 rpm
- BHP₁ (Brake Horsepower) = 20 hp
Part A
a.) If the impeller diameter is increased to D₂ = 8 in,
- Q₂ = Q₁ * (D₂ / D₁) = 100 * (8 / 6) = 133 gpm
- H₂ = H₁ * (D₂ / D₁)² = 100 * (8 / 6)² = 177 ft
- BHP₂ = 20 * (8 / 6)³ = 47 BHP
Part B
b. If the impeller diameter is increased to D₂ = 8 in and the speed is increased by 10%,
- Q₂ = Q₁ * (D₂ / D₁) * (N₂ / N₁) = 100 * (8 / 6) * (1.1) = 147 gpm
- H₂ = H₁ * (N₂ / N₁)² = 100 * (1.1)² = 121 ft
- BHP₂ = 20 * (1.1) = 22 BHP
Toluene Unloading Calculations
Example 3: A tanker carrying toluene is unloaded using ship's pumps to an on-shore storage tank. The pipeline specifications are as follows:
- Internal diameter = 225 mm
- Length = 900 m
- Miscellaneous losses = 600 equivalent pipe diameters
Given the physical properties of toluene:
- Density = 874 kg/m³
- Viscosity = 0.62 mPa s
- Pressure in ship's tanks = 1.05 bar
- Pressure in storage tank = 1.1 bar
The ship must unload 1000 metric tons within 5 hours to avoid demurrage charges. With the pump efficiency at 70%, estimate the power required by the pump.
Solution:
- Minimum fluid velocity (v) = 1.5987 m/s
- Pressure drop (ΔP) = -0.05 x 10³ Pa
- Pump power = 30076.6429 W
- Flow rate (Q) = 228.8330 m³/h
Bernoulli's Equation:
- P₁/ρ + v₁²/2 + Z₁g + Wpump = P₂/ρ + v₂²/2 + Z₂g
These calculations provide a detailed analysis of the pump's power requirements and the fluid dynamics involved in unloading toluene. The affinity laws and their applications are crucial in ensuring efficient operations in chemical engineering processes.
For more information, you can refer to the Visual Encyclopedia of Chemical Engineering Equipment, which provides a comprehensive list and design of various separation equipment and pumps used in chemical engineering processes. Additionally, the Toluene Unloading Calculations PDF offers detailed insights into the specific calculations involved in unloading toluene, ensuring the safe and efficient transfer of the chemical.
The improved text provides a clearer and organized presentation of the affinity laws sample problems and solutions, as well as the toluene unloading calculations. The content emphasizes the practical application of these principles in chemical engineering equipment design and operation. The references to additional resources add value to the reader by directing them to further information on chemical engineering equipment and specific calculations related to toluene unloading.
