pressure losses for aquahydraulic propulsion (i.e., water-based hydraulic systems) for underwater power tools i

Using aquahydraulic propulsion (i.e., water-based hydraulic systems) for underwater power tools introduces pressure losses primarily due to:

1. Hose friction loss (due to flow resistance).

2. Hydrostatic pressure increase with depth.

3. Minor losses (from bends, couplings, valves – usually negligible in general estimates).

Rules of thumb to configure the right pump:

• Most require a flow rate of 20 L/min and a local pressure of 250 Bar

• Hydrostatic pressure increases 1 bar per 10 m.

• Frictional loss is relatively small for short/vertical hoses but becomes more significant over longer runs or with higher flow rates.

• Total required pressure at 120 meters is about 12.4 bar, assuming no other losses.

• Your system must output at least this pressure to function underwater at those depths.

Pressure Loss Table

*Friction loss based on Darcy-Weisbach with water, flow of 20 L/min through a ½” hose. This is a simplification; in reality, bends and longer hoses will add more loss.

Assumptions (As input for the table):

To make a practical table, we’ll assume the following:

• Hose inner diameter (ID): ½ inch (≈12.7 mm)

• Flow rate: 20 liters per minute (L/min)

• Water temperature: 10°C (density ≈1000 kg/m³, dynamic viscosity ≈1.3 mPa·s)

• Depths: 0 to 120 meters in 10-meter increments

• Hose length: Equal to depth (i.e., vertical drop only – conservative estimate)

• Laminar flow assumed for initial calc, but we'll flag Reynolds number zones

• Friction loss calculated using the Darcy-Weisbach equation

General equation for hydrostatic pressure

Hydrostatic Pressure

$P_{\text{hydrostatic}} = \rho g h$

• $\rho = 1000\ \text{kg/m}^3$ (density of water)

• $g = 9.81\ \text{m/s}^2$

• $h$ = depth in meters

This adds a static backpressure which tools need to overcome.

Darcy–Weisbach Equation (for pressure loss due to friction in pipes):

The Darcy-Weisbach equation calculates the head loss (or pressure loss) due to friction in a pipe:

Where:

• $h_f$: frictional head loss (meters of fluid)

• $f$: Darcy friction factor (dimensionless)

• $L$: pipe length (meters)

• $D$: pipe diameter (meters)

• $v$: fluid velocity (m/s)

• $g$: gravitational acceleration (9.81 m/s²)