One of the major issues that prevent a largescale dissemination of drip irrigation system is the requirement of high pumping pressure, which incurs a high cost of pumping and power systems. The high pressure is used to maintain the working condition of pressure-compensate emitters, which are installed at the outlets of drip irrigation system to compensate pressure loss and evenly distribute flows for each crop. A new architecture of the pressure-compensate emitter is proposed using a flexible tube enclosed in a pressurized chamber similar to the design of a medical instrument called “Starling resistor”. This design enables the external pressure of the tube to correlate with the driving pressure, such that a higher driving pressure leads to a higher external pressure and consequently collapses the tube. The desirable feature that the flow rate is independent of the upstream pressure variation can be achieved with this new design at a lower driving pressure.

1. Place Graphic Here
Place Graphic Here
One of the major issues that prevent a large-
scale dissemination of drip irrigation system is
the requirement of high pumping pressure,
which incurs a high cost of pumping and power
systems. The high pressure is used to maintain
the working condition of pressure-compensate
emitters, which are installed at the outlets of drip
irrigation system to compensate pressure loss
and evenly distribute flows for each crop.
Abstract Introduction Methodology Results
A Bio-inspired Pressure Compensating Emitter for
Low-Cost Drip Irrigation Systems Ruo-Qian Wang, Amos G Winter V
Dept. of Mechanical Engineering, MIT
©Copyright, All Rights Reserved Contact: rqwang@mit.edu
Place Graphic Here
Background
Because of climate change, population growth,
urbanization, and water pollution, the world is
facing a water and food crisis. For example, the
projected annual water usage of India for 2025 is
1020 km3, among which agriculture use
contributes to 73% [1].
Drip irrigation is a potential solution
• Save 30-70% water use compared to flood
irrigation
• Increase crop yields by 23-98%
• Allow high-value crops to grow [2]
High cost prevents large-scale applications
• only 5% adoption of drip irrigation
• high cost of ~$3000/acre with solar power
• 90% of cost is power and pumping systems [2]
A technological breakthrough is needed
• Pumping power = pressure x flow rate
• Current pressure demand is 3.5 bar [2]
• Pressure compensating emitter (figure 1 & 5)
needs ~1 bar [2]
A bio-inspired design
0.2 0.4 0.6 0.8 1.0
-30
-25
-20
-15
-10
-5
~ 0.1-0.3 bar 20 40 60
∆P [cm H2O]
1
2
3
4
5
Q [liter/sec]
.
Pin Pout
Pin = Pout
NO FLOW
5
0
-5
-10
-15
-20
-25
-30
0.5 1
A / A0
Kp
∆P
b)
d)
a)
c)
Pin PoutQ
.
Pin > Pout
PRESSURE COMPENSATION
Pin
compression
e)
Pin
Pout
Pin
h
E
AA02r
L
D
FIGURE 2. Bio-inspired pressure-compensation. a) Flow rate -
pressure relationship in the human airway, as measured by Afschrift
et.al. The graphic is partially based on the image available at
http://en.wikipedia.org/wiki/File:Respiratory system complete en.svg
(accessed January 5, 2013) [8]. b) Simple model of the human airway:
a flexible tube (orange) fixed on two rigid supports (black) and placed in
a chamber open to the inlet pressure. To represent all variables used, the
valve is drawn in the pressure-compensating configuration. c) Relaxed
configuration of the valve. When the inlet and outlet pressures are
equal, there is no differential pressure acting across the flexible tube,
whose diameter is constant. d) Pressure compensating configuration.
When Pin > Pout, a difference in pressure across the flexible tube
causes its collapse and gradual variation in cross sectional area, which
obstructs the flow. e) Tube Law. The variation of cross sectional area of
a flexible cylinder with transmural pressure. Black solid line represents
empirical relationship. Orange dashed line represents equation 3 with
n = 3/2. The inset shapes represent the cross-sectional area of the tube
at various pressures. . Figure 2e) is based on Fig. 1 in [6].
pressures, the walls of the tube cave in and the response is gov-
erned by bending of the tube walls. This asymmetry is shown in
Fig. 2e. The relationship between cross sectional area and trans-
mural pressure in elastic tubes is commonly called the tube law,
and is determined experimentally [9]. However, in the interest
of simplicity, following Shapiro [6], a dimensionless analytical
expression can be fitted to the experimental curve, of the form
DP
Kp
= a n
1, (3)
where a = A/A0, A0 = pr2, n is an empirical factor between 1
and 2, and Kp represents the bending stiffness of the tube’s walls,
and is proportional to E(h/r)3. Subtracting 1 ensures there is no
predicted area change for zero transmural pressure.
The system shown in Fig. 2b,c,d is one version of a device
often called the Starling Resistor, which is a simplified but very
useful model of physiological flows in the lungs and blood ves-
sels [10].
Combining equations 2 and 3, Shapiro [6] arrived at the fol-
lowing relationship,
⇣
DP
Kp
⌘1/2
⇣
DP
Kp
+1
⌘1/n
= Q
✓
Kf
2Kp
r
A2
0
◆1/2
, (4)
which describes the relationship between the applied pressure
difference DP and the flow rate ˙Q through the tube. This ex-
pression is plotted in Fig. 3 for n ranging between 1 and 2.
In all cases, the pressure-compensating effect is strong beyond
DP/Kp ⇡ 2, which marks the activation pressure of the valve.
The case for n = 2 and DP Kp approaches the exact pres-
sure compensation as derived in the previous section. This is
evident in the asymptotic approach of the curve for n = 2 to
˙Q
⇣
Kf
2Kp
r
A2
0
⌘1/2
= 1. We note that, following Shapiro [6], we as-
sume that L µ D, that is the friction loss occurs near the exit, over
a length proportional to the smallest diameter of the constriction.
PROOF-OF-CONCEPT PROTOTYPE
To demonstrate that elastic tube deformation can result in
pressure-compensation in the range of pressures and flow rates
required by drip irrigation, we constructed a laboratory-scale
prototype of a PC valve modelled on the human airway. In this
section, we describe our methods and results of testing the pro-
totype.
Prototype Design and Construction
One benefit of the simple features of the elastic tube PC
valve design is that it can be realized in a variety of ways. In
4 Copyright c 2013 by ASME
A new architecture of the pressure-compensate
emitter is proposed using a flexible tube
enclosed in a pressurized chamber similar to the
design of a medical instrument called “Starling
resistor”. This design enables the external
pressure of the tube to correlate with the driving
pressure, such that a higher driving pressure
leads to a higher external pressure and
consequently collapses the tube. The desirable
feature that the flow rate is independent of the
upstream pressure variation can be achieved
with this new design at a lower driving pressure.
This project is aimed to find the optimal
combination of the design parameters that
govern the physics behind the collapsible tube. A
laboratory experiment has been conducted using
rubber tubes with a variety of lengths, wall
thicknesses and inner diameters. Then, an
attempt to collapse the experimental results are
made and empirical formula of activation
pressure and regulated flow rate are given.
Experiment Setup
References
[1] FAO. "Agriculture, food and water." (2003).
[2] Information provided by Jain Irrigation Ltd.
[3] Zimoch, et al. ”Bio-inspired, low-cost, self-
regulating valves for drip irrigation in developing
countries." IDETC (2013).
Acknowledgement
The authors would like to thank Jain Irrigation
Inc. and MIT Tata Center for Research and
Design for their support throughout the project.
We are exploring a new drip emitter architecture
consisting of an enclosed collapsible tube for
pressure compensation. This novel architecture
is based on a “Starling Resistor” – a means of
restricting fluid flow by applying an external
pressure to a flexible tube. Starling resistors are
commonly found throughout the human body. An
example is the bronchi in the lungs, which
collapse and make a person wheeze when they
exhale hard (see figure 4). [3]
www.sultansurgicalcenter.com
A series of experiments has been conducted to
investigate the pressure compensation of
collapsible tubes inside a pressurized chamber
(figure 6), including four factors:
• Tube length (L)
• Wall Thickness (h)
• Inner Diameter (D)
• Materials (E)
Pressure compensation
• Flow rate increases with pressure before
activation pressure
• Flow rate is independent of pressure variation
after activation pressure
• The minimum activation pressure is ~ 0.2 bar
(figure 7)
Self-excited oscillation
• Co-existing with pressure compensating
• Potentially anti-clogging
Hysteric effect
Flow rate is higher in pressure increasing
compared to pressure decreasing (arrows in
figure 7)
Figure 1 Pressure Compensating emitter
Figure 2 Water and food crisis in India
Figure 3 High pressure is needed in drip irrigation
Figure 4 Collapsible tubes in respiratory airways
Figure 5 Pressure compensation
in commercial emitter
Figure 6 Experimental
Configuration
Figure 7 Experimental results
MIT GLOBAL ENGINEERING AND
RESEARCH (GEAR) LABORATORY
GEAR.MIT.EDU
GEAR
LAB
GEAR
LAB
GEAR
LAB
GGGG
P (bar)