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:

HP = PQ / 1714

Q = (HP * 1714) / P

Determine the flow rate of a 28 HP power unit delivering 3000 PSI:

28 = (3000 * Q) / 1714

Q = (28 * 1714) / 3000 = 15.997 GPM

Determine the flow rate of a 50 HP power unit delivering 3000 PSI:

50 = (3000 * Q) / 1714

Q = (50 * 1714) / 3000 = 28.5 GPM

Determine the flow rate of a 50 HP power unit delivering 2500 PSI:

50 = (3000 * Q) / 1714

Q = (50 * 1714) / 2500 = 32.28 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
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
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
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

Pump Displacement (Cubic Inch Per Revolution, or CIPR)

Calculate the displacement for a fixed displacement as follows:

CIPR = Flow Rate (in GPM) × 231 x Pump Efficiency / Pump RPM, or:

CIPR = GPM × 231 * PE / RPM

Note: The generally accepted value for pump efficiency is 97%.

Engine hp	Formula	Pump Displacement
16	16 × 231 * 0.97 / 3600	0.996 in³ / Rev
28	28 × 231 * 0.97 / 3600	1.19 in³ / Rev
50	50 × 231 * 0.97 / 3600	2.411 in³ / Rev

Notes:

The 28 hp Briggs & Stratton engine HP is rated at 3600 RPM.
The 28 hp Renault engine HP is rated at 3000 RPM.
The 50 hp Volkswage engine HP at 3000 RPM (not sure of RPM yet