Emitter Type Determination Using Flow Parameters
The discharge ($Q$) from a drip emitter is related to the operating pressure ($P$) and the emitter constant ($K$) by the general formula:
$Q = K \cdot P^x$
The exponent '$x$' indicates the flow regime:
- $x \approx 0.5$: Turbulent flow (typical for orifices).
- $x \approx 1$: Laminar flow (typical for long-path emitters).
- $x \approx 0$: Pressure compensating emitters maintain near-constant flow regardless of pressure.
Calculate the Exponent '$x$'
Given:
- Average discharge, $Q = 4$ L h$^{-1}$
- Operating pressure, $P = 110$ kPa
- Emitter constant, $K = 0.3$
Substitute the values into the formula:
$4 = 0.3 \cdot (110)^x$
Rearrange to solve for '$x$':
1. Isolate the pressure term:
$ \frac{4}{0.3} = (110)^x $
$ 13.333... = (110)^x $
2. Take the logarithm of both sides (using natural logarithm, ln, for calculation):
$ \ln(13.333...) = \ln((110)^x) $
3. Use the logarithm power rule: $\ln(a^b) = b \cdot \ln(a)$:
$ \ln(13.333...) = x \cdot \ln(110) $
4. Solve for '$x$':
$ x = \frac{\ln(13.333...)}{\ln(110)} $
$ x \approx \frac{2.590}{4.700} \approx 0.55 $
Interpret the Result
The calculated exponent '$x$' is approximately 0.55. This value is close to 0.5, which characterises turbulent flow.
Turbulent flow is typical for simple orifice emitters where the water flows through a short opening.
Therefore, based on the calculated exponent, the emitter is most likely an orifice type.
Important Questions from Micro Irrigation Methods
- From the performance evaluation of drippers, the discharge exponent value and the coefficient of variation were obtained as 0.5 and 0.04, respectively. The drippers are categorized as
- A permanent matured orchard has a tree spacing of 4 $m\times5$ m. Each tree has a shading area of 40% to be irrigated with the 'pig tail' pattern multi-exit drip emitters. The effective wetting geometry of each emitter is 2 $m\times2$ m. The emitters have discharge constant and exponent of 0.3 and 0.6, respectively. The coefficient of variation of emitter discharge is 0.06. The average and minimum operating pressures are 120 kPa and 100 kPa, respectively. The emission uniformity of the emitters is ________ %.
- In a field test of drip irrigation system having an application efficiency of 90%, the minimum, maximum and average flow rates are found to be $45 \ L\cdot h^{-1}$, $65 \ L\cdot h^{-1}$ and $50 \ L\cdot h^{-1}$, respectively. The manufacturer's coefficient of variation of the emitter is 0.07. If there is one emitter per plant, the drip irrigation efficiency in percent is ______ [round off to 2 decimal places]
- In a citrus orchard, planting is done at a spacing of 5 m × 5 m. The daily pan evaporation of the orchard is 6 mm. The pan coefficient, wetting factor (crop canopy factor) and crop coefficient are 0.8, 0.6 and 0.6, respectively. Four drippers each of 4 L $h^{-1}$ discharge are used to irrigate each plant. The time of operation of drip irrigation system in hours will be
