Hydraulic Hose Sizing
Horsepower to Flow
First of all, we must determine fluid flow rate from the horsepower and pressure.
Horsepower = Pressure × Flow / 1714, or:
- Flow Rate (GPM): Q = (HP * 1714) / (P * 2)
- Note: SurplusCenter says for gas driven pumps, double the horsepower (or halve the flow rate for fixed hp).
- Pump Displacement (CIPR): D = Q * 231 / (RPM * 0.97)
- (CIPR = Cubic Inches Per Revolution)
| HP | RPM | PSI | Flow Formula | GPM | Displacement Formula | Displacement |
|---|---|---|---|---|---|---|
| 28 | 3600 | 3000 | (28 * 1714) / (3000 * 2) | 8 GPM | 8 * 231 / (3600 * 0.97) | 0.53 |
| 50 | 2700 | 3000 | (50 * 1714) / (3000 * 2) | 14.3 GPM | 14.3 * 231 / (2700 * 0.97) | 0.95 |
| 50 | 2700 | 2500 | (50 * 1714) / (2500 * 2) | 17.14 GPM | 17.14 * 231 / (2700 * 0.97) | 1.13 |
Note: The latest Power Cube uses a 28 hp engine and a 0.92 CIPR pump and works well, just slower than optimal. Maintaining the same ratio: 0.92/28 = CIPR/50, or CIPR = 1.64 CIPR pump for the 50 hp engine and 1.97 CIPR for a 60 hp engine. I'd like to target a CIPR between these two and the Cessna 9-4065-A is 1.78 CIPR. The only concern with this is that I'd like to operate at 2700 RPM and even though the pump specs say 3000 RPM max, it's rated flow is at 1800 RPM. It would have 20 GPM flow at 2700 RPM:
1.78 CIPR * 2700 RPM * 0.97 efficiency = 20.1 GPM
Hose Sizing
These are the formulas and guidelines for determining sizes for the three hose types: Pressure, Return and Suction. They are determined from the fluid velocity in each type of hose. There are two sets of recognized values used are:
SAE Values
- Pressure: 15 ft/sec
- Return: 10 ft/sec
- Suction: 4 ft/sec
NFP Association Values
- Pressure: 20 ft/sec
- Return: 15 ft/sec
- Suction: 5 ft/sec
The more conservative SAE values are gaining acceptance in hydraulic designers. The formula for calculating the hose size is as follows:
- V = Q / (3.117 * pi/4 * D ^ 2)
or
- D = (Q / (3.117 * pi/4 * V) ) ^ 1/2
Where:
- V is fluid velocity in ft/sec
- Q is fluid volume in gallons/min
- D is hose inside diameter in inches
Note: The sizing guidelines say to always round up.
Now, let's calculate the hose sizes:
Supply (Pressure) Hose
| Flow Rate | SAE Formula | SAE Diameter | NFP Formula | NFP Diameter |
|---|---|---|---|---|
| 13 GPM | (13 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.595 in | (13 GPM / (3.117 * pi/4 * 20 ft/sec) ) ^ 1/2 | 0.515 in |
| 16 GPM | (16 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.660 in | (16 GPM / (3.117 * pi/4 * 20 ft/sec) ) ^ 1/2 | 0.571 in |
| 20.1 GPM | (20.1 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.739 in | (20.1 GPM / (3.117 * pi/4 * 20 ft/sec) ) ^ 1/2 | 0.641 in |
| 28.5 GPM | (28.5 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.881 in | (28.5 GPM / (3.117 * pi/4 * 20 ft/sec) ) ^ 1/2 | 0.763 in |
| 32.28 GPM | (32.28 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.937 in | (32.28 GPM / (3.117 * pi/4 * 20 ft/sec) ) ^ 1/2 | 0.812 in |
Return Hose
| Flow Rate | SAE Formula | SAE Diameter | NFP Formula | NFP Diameter |
|---|---|---|---|---|
| 13 GPM | (13 GPM / (3.117 * pi/4 * 10 ft/sec) ) ^ 1/2 | 0.729 in | (13 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.595 in |
| 16 GPM | (16 GPM / (3.117 * pi/4 * 10 ft/sec) ) ^ 1/2 | 0.808 in | (16 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.660 in |
| 20.1 GPM | (20.1 GPM / (3.117 * pi/4 * 10 ft/sec) ) ^ 1/2 | 0.906 in | (20.1 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.739 in |
| 28.5 GPM | (28.5 GPM / (3.117 * pi/4 * 10 ft/sec) ) ^ 1/2 | 1.08 in | (28.5 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.881 in |
| 32.28 GPM | (32.28 GPM / (3.117 * pi/4 * 10 ft/sec) ) ^ 1/2 | 1.14 in | (32.28 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 | 0.938 in |
Suction Hose
| Flow Rate | SAE Formula | SAE Diameter | NFP Formula | NFP Diameter |
|---|---|---|---|---|
| 13 GPM | (13 GPM / (3.117 * pi/4 * 4 ft/sec) ) ^ 1/2 | 1.15 | (13 GPM / (3.117 * pi/4 * 5 ft/sec) ) ^ 1/2 | 1.03 in |
| 16 GPM | (16 GPM / (3.117 * pi/4 * 4 ft/sec) ) ^ 1/2 | 1.28 in | (16 GPM / (3.117 * pi/4 * 5 ft/sec) ) ^ 1/2 | 1.14 in |
| 20.1 GPM | (20.1 GPM / (3.117 * pi/4 * 4 ft/sec) ) ^ 1/2 | 1.43 in | (20.1 GPM / (3.117 * pi/4 * 5 ft/sec) ) ^ 1/2 | 1.28 in |
| 28.5 GPM | (28.5 GPM / (3.117 * pi/4 * 4 ft/sec) ) ^ 1/2 | 1.70 in | (28.5 GPM / (3.117 * pi/4 * 5 ft/sec) ) ^ 1/2 | 1.53 in |
| 32.28 GPM | (32.28 GPM / (3.117 * pi/4 * 4 ft/sec) ) ^ 1/2 | 1.81 in | (32.28 GPM / (3.117 * pi/4 * 5 ft/sec) ) ^ 1/2 | 1.62 in |
Notes:
The 28 hp Briggs & Stratton engine HP is rated at 3600 RPM. The 50 hp Volkswagen engine is believed to deliver the peak torque at 2700 RPM (needs confirmation)