NDT.net • June 2006 • Vol. 11 No.6

Functional Dependence of Ultrasonic Speed in Water on Salinity and Temperature

Y. N. Al-Nassar 1, A. M. Al-Jalal 2 , M. A. Khan 2, and S. A. Al-Kaabi 1
1 Mechanical Engineering Department, and, 2 Physics Department
King Fahd University of Petroleum & Minerals
Dhahran 31261, Saudi Arabia

Address for Correspondence: Prof. M. A Khan, KFUPM Box: 1947, Dhahran 31261, Saudi Arabia.
e-mail: aslamk @kfupm.edu.sa


Abstract

Investigations of functional dependence of ultrasonic speed on salinity and temperature of water samples are reported. Initially samples of saline water were prepared by dissolving measured quantities of salt (table salt, NaCl) in a given volume of de-ionized water. Measurements were carried out in a special double-walled cylindrical glass cell having plexi-glass windows. The water sample was contained in the inner tube while the surrounding annular tube was maintained at a constant temperature through a closed-loop circulation water bath. Two transducers were mounted at the two windows for launching and receiving the longitudinal ultrasonic pulses through the sample. Influence of variation of temperature on ultrasonic speed was investigated. A mathematical expression describing speed as a function of temperature and salinity is developed. This, together with the measured ultrasonic speed, was used to calculate salinity of additional samples of water collected from different locations in the Arabian Peninsula. This information may be useful in locating the sources of subsurface sweet water. The results may also be of interest in the precise location and mapping of any submerged objects.

Keywords: Ultrasonic Speed, Salinity, Waters of Arabian Peninsula

Introduction

Ultrasonic characterization of materials usually involves measurements of changes in the speed and/or the amplitude of the wave or changes in frequency spectrum of the wave as it passes through a particular medium. These parameters could be measured by analyzing the pulses transmitted through the medium or any returning echoes originating from the natural boundaries or discontinuities inside the medium.

While a lot of work has been done on inspection of materials from the point of view of locating and characterizing material defects using ultrasonic waves, there are numerous other aspects of materials characterization that could be explored using ultrasound. One interesting example is the use of ultrasound in quantifying the salt and minerals contents of seawaters. It is well known that the speed of ultrasonic waves varies considerably with the salt content and temperature. We have investigated the speed of sound as a function of salt content and temperature in laboratory-prepared as well as natural water samples. The experimental data have been used to develop a mathematical expression describing the ultrasonic speed as a function of temperature and salinity. It may be possible to develop salinity profiles of waters in the region using similar analyses. This information may be useful in locating the sources of subsurface sweet water. On the other hand, this could also help in precise location and mapping of any submerged objects.

Experimental Details

Samples of saline waters were prepared by dissolving measured quantities of salts (table salt, NaCl) in a given volume of de-ionized water. Measurements were carried out in a special double-walled cylindrical glass cell having plexi-glass windows (Fig. 1). These windows were exactly parallel to each other and perpendicular to the axis of the cell. The water sample was contained in the inner tube while the surrounding annular tube was maintained at constant temperature through a closed-loop circulation water bath. Two transducers were mounted at the two windows for launching and receiving the longitudinal ultrasonic pulses through the sample as shown in Fig. 1.

In order to use the fundamental longitudinal mode, the position of the two transducers was adjusted to be exactly at the center of the cell windows and coaxial with the water column. The transmitted signal was amplified and recorded by a digital oscilloscope. The data were transferred to an on-line PC for analysis and record. Knowing the exact distance between the transducers, transit time analysis was used to measure the speed of ultrasound. The experimental data were used to obtain a mathematical expression describing the functional dependence of speed of ultrasound on salt contents and temperature.


Fig. 1: Experimental setup

Results and Discussion

It is important to accurately find the time t taken by the ultrasonic pulse to pass through the water column. Likewise, the exact length L of the water column has to be measured with high precision. Noting that the design of the cell includes two plexi-glass windows, the signal recorded by the receiving transducer is quite complex. In particular, signals received after direct transmission as well as those reaching after suffering multiple reflections from different interfaces (plexi-glass to water, water to plexi-glass, plexi-glass to air) appear as a series of pulses (see Fig. 2a). However, it is not difficult to identify the pulse arriving directly at time t1 (fundamental longitudinal mode). Likewise, the pulse arriving after direct transmission through the first window and the water to plexi-glass interface (second window) but suffering first reflection at the plexi-glass to air interface of the second window and subsequently at its back surface (plexi-glass to water interface), appears at time t2. The pulse reflected at the plexi-glass to water interface of first window and subsequent reflection at its back surface (plexi-glass to air interface) followed by through-transmission thereafter, also appears at time t2. Pulses suffering other reflections will take considerably longer times and are not considered in this analysis. Fig. 2b shows an illustration of the corresponding rays discussed above.

The time taken by the ultrasonic wave to pass through the column of water was calculated to be t1 - (t2-t1) or 2t1 - t2. The speed V of the ultrasound can now be calculated from

V = L / (2t1 - t2) (1).

Speed of ultrasound in saline waters as a function of salt content

Initially, we prepared salt solutions in de-ionized water using different quantities of table salt, namely, 0, 25, 50, 75, 100, 125, 150 and 200 grams/liter. The temperature of the solution was maintained constant at 22 °C. A graph between the speed of ultrasound and salt concentration was plotted (Fig. 3). A linear fit to the data gave the following expression describing the ultrasonic speed V (m/s) as a function of concentration C (g / l) at a temperature of 22 °C.

V(C) = 0.94 C + 1480.5     (2)

This expression was used to determine the salt content (NaCl-equivalent) of waters of Arabian Peninsula. In particular, samples of seawater from Azizia (Al-Khobar), Khafji, Jubial, Bahrain, Dead Sea, as well as Al-Khobar sweet water, Zam-Zam, and rainwater were investigated. Table 1 presents a summary of the results on salt contents of these water samples.


Fig. 2a: Examples of ray tracing indicating some possible reflections and transmissions at various interfaces.


Fig. 2b: Sequence of some pulses seen by the receiving transducer.


Figure 3: Speed of ultrasonic waves in saline water as a function of salt concentration at 22 °C.

Table 1 : Salinity of waters of Arabian Peninsula.
Sourse V (m/s) at 22 °C C (g/l)
Azizia (Al-Khobar) sea water 1539 65.9
Khafji sea water 1524 49.5
Jubail sea water 1524 49.5
Bahrain 1526 52.0
Dead Sea 1789 331
Al-Khobar sweet water 1478 0.51
Zam-Zam water 1478 1.02
Rainwater (KFUPM, Dhahran) 1478 1.02
De-ionized water 1477 0.0

In general, no data have been published on the salinity of Arabian waters except for the salinity of Dead sea water [1]. Our results are in good agreement with the values reported therein. Interestingly, according to our measurements, the salt content of Zam-Zam water appears to be the same as the rainwater. This is significant in the sense that it indicates the source of Zam-Zam.

Speed of ultrasound in saline waters as a function of temperature

Further experimental measurements were carried out on the speed of ultrasound using similar concentrations of salt in de-ionized water but at different temperatures, namely, 10, 20, 30,40, 50, and 60 °C. The curves showing the speed of ultrasound as a function of temperature are presented in Fig. 4. The corresponding mathematical expressions describing the speed as a function of temperature for different salt contents are:

V(T) = 62.4 ln (T) + 1285.6     at C = 0 g/l     (3.1)

V(T) = 41.7 ln (T) + 1449.5     at C = 100 g/l     (3.2)

V(T) = 35.3 ln (T) + 1515.4     at C = 150 g/l     (3.3)

V(T) = 26.7 ln (T) + 1581.1     at C = 200 g/l     (3.4)

This is a logarithmic dependence. However, the logarithmic function can also be written as a power series as done for pure water in some earlier work [2].

Combining the functional dependences of speed V on the concentration C and temperature T, we obtained the following mathematical relation

V(C, T) = S1 (C) + S2 (C) ln (T)     (4)

Here,

S1 (C) = 1285.6 + 2.0105 C -0.0048 C2 +1× 10-5 C3     (4.1a)

S2 (C) = 62.4 - 0.3322 C + 0.0017 C2 - 5 × 10-6 C3     (4.2a),

with an R2 value of 1 for both expressions. It seems from the two expression that they can be approximated to quadratic form since the coefficients in the third power are very small. In that case, the expressions take the following form with a slight decrease in the value of R2.

S1 (C) = 1285.9 + 1.7661 C - 0.0015 C2     (4.1b)

S2 (C) = 62.268 - 0.2197 C + 0.0002 C2     (4.2b)

Previously, Bilaniuk and Wang [1] and Dushaw et al [2] have given a polynomial of fifth order to describe the speed of sound in pure water as function of temperature. Our results are in good agreements with the functional dependence predicted in [2-3].

It may be remarked that precise information on functional dependence of speed of ultrasound on salinity and temperature could help in developing salinity profiles of waters in the Arabian Peninsula. This information may be useful in locating the sources of sub-surface sweet water. This could also help in precise location and mapping of any submerged objects


Figure 4: Speed of ultrasound in saline water as a function of temperature for different salt concentration.

Conclusions

A mathematical expression describing the speed of ultrasound in waters of Arabian Peninsula as a function of salinity and temperature has been developed. It may be possible to develop salinity profiles of waters in the region using similar analysis. This information may be useful in locating the sources of sub-surface sweet water. This could also help in precise location and mapping of any submerged objects.

Acknowledgements

The support provided by Energy Research Center, College of Sciences, King Fahd University of Petroleum and Minerals, is gratefully acknowledged. The help of Mr. Ayman Ghannam of Physics Department in obtaining the sample of Dead Sea water is also acknowledged.

References

  1. N. Bilaniuk and G. S. K. Wong, "Speed of sound in pure water as function of temperature", J. Acoust. Soc. Am., 93(3), 1609-1612. (1993).
  2. B. D. Dushaw, P. F. Worcester, B. D. Cornuelle, and B. M. Howe, "On equation for the speed of sound in seawater," J. Acoust. Soc. Am., 93, 255-275 (1993).
  3. V. A. DelGrosso, "Tables of the speed of sound in open ocean water (with Mediterranean Sea and Red Sea applicability)," J. Acoust. Soc. Am. 53, 1384-1401(1973).

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