Machine Design

# SPEED LIMITS: Relating flow velocity to hydraulic performance

Too slow a flow means a sluggish system, and too fast causes damage and leaks.

## SPEED LIMITS: Relating flow velocity to hydraulic performance

Peter J. Stroempl
Engineering Manager
Parker Hannifin Corp.
Stratoflex Products Div.
Ft. Worth, Tex.

 Designers should always consider flow velocity through hose and tubing to optimize performance while avoiding excessive losses or pressure spikes. This aerospace high-pressure pump installation includes suction, pressure, and drain lines.

A key parameter for most hydraulic and fluid systems is flow velocity though hose or pipe. Designers usually strive to maximize flow, optimizing performance while using the smallest possible hose to save on cost, space, and weight. But too high a fluid bulk flow velocity may cause excessive pressure drop or damaging pressure spikes.

Unfortunately, flow velocity doesn't seem to get the attention it deserves. For instance, typical hose-qualification procedures include burst, flex, and impulse testing, but usually not flow testing. Fluid-dynamics textbooks generally do not offer fluid flow-velocity guidelines. They merely advise designers to size a hose to avoid excessive pressure drop. But design criteria such as pressure rating and pressure peaks must be evaluated independent of pressure drop. Flow capacity and pressure limits often depend on the actual application. Several hydraulic-component suppliers also publish fluid bulk-flow-velocity guidelines, but none cites the fundamental testing used to validate-the numbers.

To clarify the impact flow velocity has on hydraulic-system performance, here's a closer look at the data needed to properly size hose and pipe.

FLOW BASICS
Fluid bulk flow velocity vbis the volume flow rate through a hose or other fluid conduit divided by the cross-sectional area of the flow passage.

Typical units of bulk flow velocity are ips or fps.

Bulk modulus b indicates the relationship when pressure rises ΔP as fluid compresses (ΔV) in a pressure vessel of volume Vo.

The negative sign indicates fluid compression.

Note there are actually three types of bulk modulus: the secant bulk modulus b as well as tangent and effective bulk moduli (Keller, George R., " Hydraulic System Analysis," Penton Publications, 1978). The secant bulk modulus at isothermal and isentropic conditions is an average taken across a range of ΔP/(ΔV/Vo) values. The tangent bulk modulus at isothermal and isentropic conditions is the value as V approaches zero and ΔP/ΔV approaches its limit. Effective bulk modulus is an experimental value taken for a specific system configuration.

Shock relates to the system and pressure-reliefvalve performance. It can be defined as:

Hydraulic and other fluid systems usually contain devices that limit pressure swings that result from dynamic events — valves opening or closing, actuators starting or stopping, and so on. Pressure-control valves typically respond quickly. Small relief valves may fully open in about 6 to 30 msec. Larger relief valves may take 60 to 100 msec. During that short time the pump continues to discharge fluid, and that flow must be absorbed by fluid conductors, valves, actuators, and other components. System pressure rises because pressure controls do not anticipate but respond to the additional flow.

Shock is related to bulk modulus — the stiffer the system, the higher the shock pressure. In all cases, shock can damage components and cause leaks.

Illustrating the effects of fluid velocity This example shows what happens to the pressure level inside a hose assembly as the pressure-control device response and fluid bulk flow velocity vary.

Assume: b = 43,785 psi/in. 3/in. 3, L0 = 80 in., and valve-pressure setting P0 = 1,000 psi. Also, assume the fluid-flow column comes to a sudden stop at the end of 80 in. of travel.

Values in the table assume that the relief valve with a 50 msec setting time opens and exhausts flow about 12 msec after flow is cut off at the end of the hose length. During that time, the hose must absorb the flow discharged from the pump until the relief valve opens. The last two lines show that a faster relief valve (6 msec response, 25 msec setting time) reduces shock. Conversely, a slower valve in a system with a high fluid bulk flow velocity increases shock pressure.

The results are straightforward. All else being equal, a higher fluid bulk flow velocity means a greater pressure spike. Note that at high bulk flow velocity, pressure levels may spike above operational levels before the pressure-control device opens.

 How Flow Velocity Affects Pressure Fluid bulk flow velocity (vb), ips Pressure-control response, sec Size of pressure spike, psi Base pressure setting, psi Total pressure (base + spike), psi 120 0.012 788 1,000 1,788 300 0.012 1,970 1,000 2,970 600 0.012 3,941 1,000 4,941 300 0.006 985 1,000 1,985 600 0.030 9,852 1,000 10,852

FLUID BULK FLOW VELOCITY
The compression-induced change of volume equals the fluid bulk flow rate through the conduit summed over the time required for the pressurecontrol device to relieve or divert flow to another path,

In other words, ΔV is the amount of fluid that compresses while the pressure-control system responds. The slower the response, the more the fluid compresses. As a consequence, the potential pressure spike ΔP that develops as the pressurecontrol device responds is:

where vessel volume, V0 = (p/4)D 2 L0, and L0 = hose length or fluid-column length under compression.

For a given system with all else being equal, pressure spike is directly proportional to the fluid bulk flow velocity, ΔP avb.

To relate fluid bulk flow velocity to the potential pressure-spike height, express the relationship as:

Hose, fluid, and other system components have capacitance. The hose assembly expands under pressure and fluid compresses slightly. These two elements together behave like springs in parallel. This equation defines the relationship between pressure rise, hose or system bulk modulus, and fluid velocity. It provides a means to evaluate possible flow-induced system shock and helps illustrate why bulk-flow limits should be observed.

Determining flow capacity

The nomogram provides an aid in determining the correct hose size. For instance, to find the proper hose size for a 16-gpm pressure line, locate 16 gpm in the left column and 20 fps in the right column. A line connecting the two points shows the required hose ID would be 0.625 in. or larger.

The nomogram is based on:

where Q=flow, gpm: v=velocity, fps; and D= hose ID, in.

BULK MODULUS AND FLUID VELOCITY
The relationship above indicates the impact of fluid bulk flow velocity. For instance, take the example where bulk modulus (b ) of the hose and fluid is held constant. (This value must be determined experimentally.) Then consider several cases:

Case 1: Lengthen the hose assembly. Increasing hose length Lo softens the pressure spike by creating more hose volume Vo. The extra volume absorbs the additional pumped fluid. Lengthening the hose segment is one way to soften pressure spikes.

Case 2: Hold b , Lo, and Δt constant. Then the pressure spike is directly proportional to vb. In other words, the faster the fluid bulk flow rate, the greater the spike pressure. For example, when vb= 50 fps, the pressure spike is twice as large as in a system where vb= 25 fps.

Case 3: Increase pressurecontrol device response. ΔP is proportional to ∑vbΔt. Not surprisingly, at a fluid bulk flow velocity of 50 fps, twice the fluid flows through the hose segment per unit time than at 25 fps. Therefore, shortening the system's pressure-control-device response will soften the pressure spike. So a device that responds in 30 msec will allow about half as much fluid to flow through a hose segment as a pressure control device that responds in 60 msec.

Keep in mind there are limiting factors. Designs must be based on the loop pressure drop at the lowest required operating temperature and the highest possible bulk flow velocity to minimize pressure-drop losses as well as plumbing size and weight.

Also, be careful when evaluating back pressure in the return line. High back pressure in the return line may affect brake or valve behavior, or actuator function. For example, back pressure in the return line adds to forces generated by valve-bias springs.

 SUGGESTED FLUID BULK VELOCITIES These recommendations are not hard limits, but provide a starting point for the system designer. Actual velocity limit depends upon the application and performance of the pressure-control devices. Also note that in mobile installations be aware of fluid viscosity at low temperature. SUBSYSTEM BULK VELOCITY GUIDELINE, fps Suction lines (industrial installation) 5 Suction lines (mobile installation) 8 Pressure (working) lines 30 Return lines 15 Pump and valve-case drain lines 10

RECOMMENDATIONS
Bulk flow velocity must be determined empirically. However, the accompanying tables show general guidelines from various sources in the public domain.

In the absence of special pressure-control provisions, the rules of thumb from the "Summary of recommendations" table are suitable for general applications to minimize shock. It remains incumbent upon designers to demonstrate the suitability of the information for a particular application.

The "Suggested fluid bulk velocities" table gives system designers a good-starting point, but not hard limits. Experiments and experience with flow velocities above or below these suggested levels let the designer determine what works best for an application.

In the end, the design bulk flow velocity must be matched to components and required system performance. Key parameters are the hose (or control volume) length and system-related bulk modulus on one hand, and the bulk flow velocity on the other. A slower fluid bulk flow velocity reduces shock. Similarly, a longer hose assembly means a smaller shockpressure rise — all else being equal. Fast-acting pressure-control devices also permit higher fluid bulk flow velocities.

 SUMMARY OF RECOMMENDATIONS APPLICATION RECOMMENDED BULK FLOW RATE, fps SOURCE Hydraulic and lubrication systems Atmospherically aspirated pump Industrial return-line flow Pressure line flow To 8 fps To 10 fps (to maximize back pressure) To 20 fps Parker Hannifin Catalog 4400, p. G10 Pressure/supply-line flow To 30 fps Womack's "Fluid Power Data Book" Pressure-line flow To 15 fps (With successful applications to 30 fps) SAE ARP994, para. 4.1.1 Rules of thumb from PH Aerospace Pump Div. To 8 fps for pump suction. To 30 fps for supply lines. To 15 fps for return lines. PH Aerospace Pump Div. Applications Engineering Group. Lubrication-system flow To 10 fps Use hydraulic-system design principles Special Systems Flow through a convoluted annular metal hose assembly Gas, <150 fps Liquid, <75 fps PH Stratoflex Products Div.; Type AS1424 hose assemblies Pneumatic Systems Pneumatic flow Mach number <0.3 One-dimensional, compressible flow with a Mach number <0.3 may be treated as incompressible flow. Fuel Systems Engine-fuel application To 30 fps Note that low vapor pressure makes fuels susceptible to cavitation. Consider the Euler Number (and related Cavitation Parameter) to determine a fuel's acceptable bulk flow velocity. The table summarizes data available from various sources. The rules of thumb provide guidelines to minimize shick in general applications, but flow limits will vary depending on the actual system.
TAGS: Hydraulics
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