- Email: [email protected]
The viscosity of liquid hydrogen
P h y s i c a V, no 8
A u g u s t u s 1938
THE VISCOSITY OF LIQUID HYDROGEN b y W. H. KEESOM and G. E. MACWOOD *) Commun. No. 254b from the Kamerlingh Onnes Laboratory at Leiden Summary An e x p e r i m e n t a l verification is g iv e n of t h e corrections given b y one of us 1) for viscosities d e t e r m i n e d b y t h e oscillating disc method. We, also, r e p o r t the viscosity of liquid h y d r o g e n in the t e m p e r a t u r e range from 14.8 ° to 20.0oK.
§ I. Introduction. Continuing the program of research on the viscosity of gases and liquefied gases 2), we report our results on liquid hydrogen. In order to test the theory of the oscillating disc as developed b y on.e of us 1) 3), the viscosity of liquid hydrogen was measured in the extreme" cases of large and small disc separations. These measurements serve to show the applicability of the method *in the case of liquid helium 2).
§ 2. Apparatus and method o/ measurement. The apparatus employed is the same as used for liquid helium and has been described previously 2). The values of the logarithmic decrement are average values, each being calculated from about 15 complete oscillations. The period was determined b y means of a stop-watch, taking the 15th part of the time of 15 complete oscillations. The watch could be read to 0.02 sec. and was checked against the Observatory clock.
§ 3. Measurements o/ liquid hydrogen. The constants of the apparatus were determined b y measurements with helium g~s as described previously 2). In these measurements, we observed 10 to 15 oscillations for *) National Research Fellow, Cutting Traveling Fellow of Columbia University.
- - 745 - -
746
W. H. K E E S O M AND G. E. MACWOOD
each point from which the period and logarithmic decrement were obtained. The temperature was obtained by means of a vapour pressure thermometer, using the vapour pressures reported b y Keesom, B i j l and Miss v a n d e r H o r s t 4 ) . T h e d e n s i t y o f liquid hydrogen is required in the reduction of the experiments and the values of K a m e r l i n g h Onnes and C r o m m e l i n s ) were used. In order to check the theory of the apparatus *) 3), we made measurements at two different disc separations, 0.06 cm and 1.5 cm. In Tables I and n are given the results for the two cases. TABLE I
lVleasurements with small disc separation Viscosity of liquid hydrogen with small disc separation
Date 1938 30 March
Temp. °K 14.85 14.88 14.92 15,89 16.28 16.35
17.68 17.77 18.75 18.78
Period sec.
Log.
Uncorrected
190.6 189.6 186.6 169.4 164.0 162.0
213.2 212.1 208.7 189.5 183.4 181.3 157.0 156.0 142.4 141.7
Decrement x 10~
24.71 24.705 24.71 24.70 24.69 24.70 24.71 24.69 24.71 24.71
Corrected
Viscosity [~ poise
140.3 139.4
127.3 126.7
Viscosity ~. poise
J
216.2
216.0 212.6 193.2 187.0 184.9 160.3 159.3 145.6
144.8
TABLE II
Measurements with large separation Viscosity of liquid hydrogen with large disc separation
Date 1938 5 April
Temp. °K
Period sec.
14.83 15.39
24.93
16.40 17.06 1'7.74 18.38 18.95 19.66 20.00
24.86 24.90 24.84 24.88 24.89 24.81 24.88 24.88
Log. Decrement x 103
j
83.00 79.80 74.71 72,60 69.10 66.92 64.86 63.39 63.14
Uncorrected I Corrected Viscosity Viscosity V- poise J t~ poise 249.7 230.6 207.6 195.0 179.5 169.7 159.2 155.2 154.9
215.0 200.1 182.2 171.5
159.2 151.0 143.0 139.2
138.8
In Fig. 1 is shown the viscosity of liquid hydrogen determined in the two cases. Curve (~ shows the values for large disc separations
T H E VISCOSITY OF LIQUID H Y D R O G E N
747
(
according to the simple theory 3) and curve (D the same for small separations. Curve Q & gives the corrected values 1) for both cases.
\
o\ \ \
T
16
tS
17
t8
tS
F i g . 1. V i s c o s i t y o f l i q u i d h y d r o g e n . (D A (b Q ~X
-- Small separation -- Small separation -- Large separation -- Large separation --Verschaffelt
-----
uncorrected corrected uncorrected corrected
§ 4. Conclusion. The results show rather nicely the applicability of the method for determining the viscosity of a liquid and the consistency of the two methods of measurements. Verschaffelt and N i c a i s e 6 ) have reported one value of the viscosity of liquid hydrogen at its boiling point. This value is shown in Fig. 1. The accuracy of this value is about 10% according to V e r s c h a f f e l t . The viscosity of liquid hydrogen appears to be quite normal *), *) The value of the viscosity of hydrogen calculated from the law of corresponding states v) in connection with the viscosity of liquid oxygen ~) agrees to within 4% with the observed value at 20°K.
748
T H E VISCOSITY O F LIQUID H Y D R O G E N
and no definite evidence was obtained to decide whether it exhibits slip. In the results reported here, we have assumed that the slip is zero. § 5. Acknowledgements. It is with pleasure that we record our thanks to the Smithsonian Institution for a grant-in-aid, and to J. H. S c h w e e r s , phil. nat. drs., and P. H. K e e s o m , phil. nat. cand., for their help during the measurements and with the calculations. Received June 28th, 1938.
REFERENCES I) G. E. M a e W o o d , Commun. Kamerlingh Onnes Lab., Leiden Suppl. No. 84c; Physica 5, 763, 1938. 2) W. H. K e e s o m and G. E. M a c W o o d , Commun. Kamerlingh Onnes Lab., Leiden, No. 254a, Physica 5, 737, 1938. 3) G. E. M a c W o o d , Commun. Kamerlingh Onnes Lab., Leiden Suppl. No. 84b; Physica 5, 374, 1938. 4) W. H. K e e s o m , A. B i j l and Miss H. v a n d e r H o r s t , Commun. Kamerlingh Onnes Lab., Leiden No. 217a; Proc. Kon. Akad. A m s t e r d a m 34, 1223, 1931. 5) H. K a m e r l i ~ g h Onnes and C. A. C r o m m e l i n , Commun. Kamerlingh Onnes Lab., Leiden No. 137a; Proc. Kon. Acad. A m s t e r d a m , 214, 1913. 6) J. E. V e r s c h a f f e l t and C. N i c a i s e , Commun. Kamerlingh Onnes Lab., Leiden No. 151g; Proc. Kon. Akad. A m s t e r d a m 25, 1224, 1917. 7) H. K a m e r l i n g h Onnes, Commun. Kamerfingh Onnes Lab., Leiden No. 12. 8) N. S. R u d e n k o and L. W. S c h u b n i k o w , Phys. Z. Sowjetunion, Charkow 1936, Sondernummer, p. 83.
A u g u s t u s 1938
THE VISCOSITY OF LIQUID HYDROGEN b y W. H. KEESOM and G. E. MACWOOD *) Commun. No. 254b from the Kamerlingh Onnes Laboratory at Leiden Summary An e x p e r i m e n t a l verification is g iv e n of t h e corrections given b y one of us 1) for viscosities d e t e r m i n e d b y t h e oscillating disc method. We, also, r e p o r t the viscosity of liquid h y d r o g e n in the t e m p e r a t u r e range from 14.8 ° to 20.0oK.
§ I. Introduction. Continuing the program of research on the viscosity of gases and liquefied gases 2), we report our results on liquid hydrogen. In order to test the theory of the oscillating disc as developed b y on.e of us 1) 3), the viscosity of liquid hydrogen was measured in the extreme" cases of large and small disc separations. These measurements serve to show the applicability of the method *in the case of liquid helium 2).
§ 2. Apparatus and method o/ measurement. The apparatus employed is the same as used for liquid helium and has been described previously 2). The values of the logarithmic decrement are average values, each being calculated from about 15 complete oscillations. The period was determined b y means of a stop-watch, taking the 15th part of the time of 15 complete oscillations. The watch could be read to 0.02 sec. and was checked against the Observatory clock.
§ 3. Measurements o/ liquid hydrogen. The constants of the apparatus were determined b y measurements with helium g~s as described previously 2). In these measurements, we observed 10 to 15 oscillations for *) National Research Fellow, Cutting Traveling Fellow of Columbia University.
- - 745 - -
746
W. H. K E E S O M AND G. E. MACWOOD
each point from which the period and logarithmic decrement were obtained. The temperature was obtained by means of a vapour pressure thermometer, using the vapour pressures reported b y Keesom, B i j l and Miss v a n d e r H o r s t 4 ) . T h e d e n s i t y o f liquid hydrogen is required in the reduction of the experiments and the values of K a m e r l i n g h Onnes and C r o m m e l i n s ) were used. In order to check the theory of the apparatus *) 3), we made measurements at two different disc separations, 0.06 cm and 1.5 cm. In Tables I and n are given the results for the two cases. TABLE I
lVleasurements with small disc separation Viscosity of liquid hydrogen with small disc separation
Date 1938 30 March
Temp. °K 14.85 14.88 14.92 15,89 16.28 16.35
17.68 17.77 18.75 18.78
Period sec.
Log.
Uncorrected
190.6 189.6 186.6 169.4 164.0 162.0
213.2 212.1 208.7 189.5 183.4 181.3 157.0 156.0 142.4 141.7
Decrement x 10~
24.71 24.705 24.71 24.70 24.69 24.70 24.71 24.69 24.71 24.71
Corrected
Viscosity [~ poise
140.3 139.4
127.3 126.7
Viscosity ~. poise
J
216.2
216.0 212.6 193.2 187.0 184.9 160.3 159.3 145.6
144.8
TABLE II
Measurements with large separation Viscosity of liquid hydrogen with large disc separation
Date 1938 5 April
Temp. °K
Period sec.
14.83 15.39
24.93
16.40 17.06 1'7.74 18.38 18.95 19.66 20.00
24.86 24.90 24.84 24.88 24.89 24.81 24.88 24.88
Log. Decrement x 103
j
83.00 79.80 74.71 72,60 69.10 66.92 64.86 63.39 63.14
Uncorrected I Corrected Viscosity Viscosity V- poise J t~ poise 249.7 230.6 207.6 195.0 179.5 169.7 159.2 155.2 154.9
215.0 200.1 182.2 171.5
159.2 151.0 143.0 139.2
138.8
In Fig. 1 is shown the viscosity of liquid hydrogen determined in the two cases. Curve (~ shows the values for large disc separations
T H E VISCOSITY OF LIQUID H Y D R O G E N
747
(
according to the simple theory 3) and curve (D the same for small separations. Curve Q & gives the corrected values 1) for both cases.
\
o\ \ \
T
16
tS
17
t8
tS
F i g . 1. V i s c o s i t y o f l i q u i d h y d r o g e n . (D A (b Q ~X
-- Small separation -- Small separation -- Large separation -- Large separation --Verschaffelt
-----
uncorrected corrected uncorrected corrected
§ 4. Conclusion. The results show rather nicely the applicability of the method for determining the viscosity of a liquid and the consistency of the two methods of measurements. Verschaffelt and N i c a i s e 6 ) have reported one value of the viscosity of liquid hydrogen at its boiling point. This value is shown in Fig. 1. The accuracy of this value is about 10% according to V e r s c h a f f e l t . The viscosity of liquid hydrogen appears to be quite normal *), *) The value of the viscosity of hydrogen calculated from the law of corresponding states v) in connection with the viscosity of liquid oxygen ~) agrees to within 4% with the observed value at 20°K.
748
T H E VISCOSITY O F LIQUID H Y D R O G E N
and no definite evidence was obtained to decide whether it exhibits slip. In the results reported here, we have assumed that the slip is zero. § 5. Acknowledgements. It is with pleasure that we record our thanks to the Smithsonian Institution for a grant-in-aid, and to J. H. S c h w e e r s , phil. nat. drs., and P. H. K e e s o m , phil. nat. cand., for their help during the measurements and with the calculations. Received June 28th, 1938.
REFERENCES I) G. E. M a e W o o d , Commun. Kamerlingh Onnes Lab., Leiden Suppl. No. 84c; Physica 5, 763, 1938. 2) W. H. K e e s o m and G. E. M a c W o o d , Commun. Kamerlingh Onnes Lab., Leiden, No. 254a, Physica 5, 737, 1938. 3) G. E. M a c W o o d , Commun. Kamerlingh Onnes Lab., Leiden Suppl. No. 84b; Physica 5, 374, 1938. 4) W. H. K e e s o m , A. B i j l and Miss H. v a n d e r H o r s t , Commun. Kamerlingh Onnes Lab., Leiden No. 217a; Proc. Kon. Akad. A m s t e r d a m 34, 1223, 1931. 5) H. K a m e r l i ~ g h Onnes and C. A. C r o m m e l i n , Commun. Kamerlingh Onnes Lab., Leiden No. 137a; Proc. Kon. Acad. A m s t e r d a m , 214, 1913. 6) J. E. V e r s c h a f f e l t and C. N i c a i s e , Commun. Kamerlingh Onnes Lab., Leiden No. 151g; Proc. Kon. Akad. A m s t e r d a m 25, 1224, 1917. 7) H. K a m e r l i n g h Onnes, Commun. Kamerfingh Onnes Lab., Leiden No. 12. 8) N. S. R u d e n k o and L. W. S c h u b n i k o w , Phys. Z. Sowjetunion, Charkow 1936, Sondernummer, p. 83.