# 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
7 3600 3000 (7 * 1714) / (3000 * 2) 2 GPM 2 * 231 / (3600 * 0.97) 0.132
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
65 2700 3000 (65 * 1714) / (2500 * 2) 18.57 GPM 18.57 * 231 / (2700 * 0.97) 1.637

I haven't been satisfied with these numbers, as the displacement seems too small and would likely result in not enough flow. It is only an 18.6% increase in displacement even though the horsepower has doubled and the RPM is 25% lower.

In the past, the preferred power for the LifeTrac has employed ~54 horsepower @ 3600 RPM to drive two pumps, each about 0.92 cu in displacement. This has proven satisfactory and is the rule against which the new Power Cube will be measured. The total pump displacement was 1.84 CIPR (Cubic Inches Per Revolution). This gives a ratio of HP:Flow of 54:(1.84 * 3600).

For the new Power Cube, the engine will be producing between 50 and 60 hp @ 2700 RPM (the RPM yielding max torque). So, using the above ratio to derive the new displacement as follows for 50, 60 HP @ 2700 RPM and 51 HP @ 1800 RPM:

```54:(1.84 * 3600) = 50:(R * 2700)
-or-
R = 50 * 1.84 * 3600 / (54 * 2700) = 2.271 CIPR
```
```54:(1.84 * 3600) = 60:(R * 2700)
-or-
R = 60 * 1.84 * 3600 / (54 * 2700) = 2.726 CIPR
```

So, this "rule of thumb" measurement puts the displacement at about 2.5 CIPR and 28.3 GPM flow:

```2.5 * 0.97 * 2700 / 231 = 28.34
```

Here is the case for a 51 hp engine at 1800 RPM:

```54:(1.84 * 3600) = 51:(R * 1800)
-or-
R = 60 * 1.84 * 3600 / (54 * 1800) = 4.008 CIPR
```

So, this "rule of thumb" measurement puts the displacement at about 2.5 CIPR and 30.23 GPM flow:

```4 * 0.97 * 1800 / 231 = 30.23 GPM
```

Finally, the case for a 65 hp engine at 1800 RPM (pulley reduced RPM from 2700 @ engine to 1800 @ pump):

```54:(1.84 * 3600) = 65:(R * 1800)
-or-
R = 65 * 1.84 * 3600 / (54 * 1800) = 4.43 CIPR
```

So, this "rule of thumb" measurement puts the displacement at about 4.4 CIPR and 30.23 GPM flow:

```4.4 * 0.97 * 1800 / 231 = 33.2 GPM
```

Here is the case for a 7 HP engine running at 3600 RPM:

```7:(1.84 * 3600) = 51:(R * 3600)
-or-
R = 7 * 1.84 / 54 = 0.238 CIPR
```

## Pump Sizing

With all this in mind, in my first thought this is the closest pump I found:

After some discussion with people who have operated the LifeTrac (the target machine for this power cube), there seems to be need for separating flow between right track, left track and the accessories (loader arms, etc). To this end, I found that typical skid steer equipment use triple or quadruple pumps and separate circuits for driven equipment. A little more digging turned up these double and triple pumps used on Bobcat equipment:  Bobcat Double Pump Bobcat Triple Pump

James Slade and I have discussed this at some length and decided that we'd like to use pumps and hydraulic motors similar to those in other skid steer equipment - such as those listed above. We do need some details about each of the three pumps in the "triple pump":

```Max/Rated RPM
Max/Rated PSI
Rated GPM for each
```

As well as the pump dimensions, weight and operating characteristics of the built-in pressure relief valve.

It is not clear yet what the type of pumps used, but one article indicates that the tracks are driven by variable-displacement pumps and the arms & accessories driven by fixed-displacement pumps.

Note: Using multiple pumps to drive isolated circuits would result in multiple separate circuits - each with smaller hose sizes and associated plumbing. The suction plumbing could be aggregated to simplify the design to use a single suction strainer and hose. Similarly, the return plumbing could be aggregated to use a single oil cooler and return filter.

## 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
48 GPM (48 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 1.114 in (48 GPM / (3.117 * pi/4 * 20 ft/sec) ) ^ 1/2 0.99 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
48 GPM (48 GPM / (3.117 * pi/4 * 10 ft/sec) ) ^ 1/2 1.4 in (48 GPM / (3.117 * pi/4 * 15 ft/sec) ) ^ 1/2 1.114 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
48 GPM (48 GPM / (3.117 * pi/4 * 4 ft/sec) ) ^ 1/2 2.21 in (48 GPM / (3.117 * pi/4 * 5 ft/sec) ) ^ 1/2 1.98 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)
This increased fluid flow requires quick couplers capable of handling more flow. This coupler is rated for 26.4 GPM: ```