Water at 50^◦ C is lifted from a tank to a higher elevation by the use of a siphon tube. (a) Determine the minimum pressure in the siphon tubing in order to avoid cavitation.

Question

Water at [latex]50^{\circ } C[/latex] is lifted from a tank to a higher elevation by the use of a siphon tube. (a) Determine the minimum pressure in the siphon tubing in order to avoid cavitation.

Accepted Answer

(a) Cavitation will occur if the pressure of the water in the siphon tubing system is allowed to drop below the vapor pressure of the water at [latex]50^{\circ } C[/latex], which is read from Table A.2 in Appendix A as follows:

[latex]p_{\upsilon } =12.33kN/m^{2} abs[/latex]

Thus, the minimum pressure in the siphon tubing in order to avoid cavitation is given as follows:

[latex]p_{min} =p_{\upsilon }=12.33kN/m^{2} abs[/latex]

Table A.2
Physical Properties for Water at Standard Sea-Level Atmospheric Pressure as a Function of Temperature
Temperature (θ) [latex]^{\circ } F[/latex]	Density (ρ) [latex]slug/ft^{3} [/latex]	Specific Weight (γ) [latex]Ib/ft^{3}[/latex]	Absolute (Dynamic) Viscosity (μ) [latex]10^{-6} Ib-sec/ft^{3}[/latex]	Kinematic Viscosity (ν) [latex]10^{-6} ft^{2}/sec[/latex]	Surface Tension (σ) lb=ft	Vapor Pressure [latex]( ho _{ u } )[/latex] psia	Bulk Modulus of Elasticity [latex](E_{\upsilon } )[/latex] psi
32	1.940	62.42	37.46	19.31	0.00518	0.0885	293.000
40	1.940	62.43	32.29	16.64	0.00514	0.1220	294.000
50	1.940	62.41	27.35	14.10	0.00509	0.1780	305.000
60	1.938	62.37	23.59	12.17	0.00504	0.2560	311.000
70	1.936	62.30	20.50	10.59	0.00498	0.3630	320.000
80	1.934	62.22	17.99	9.30	0.00492	0.5070	322.000
90	1.931	62.11	15.95	8.26	0.00486	0.6980	323.000
100	1.927	62.00	14.24	7.39	0.00480	0.9490	327.000
110	1.923	61.86	12.84	6.67	0.00473	1.2750	331.000
120	1.918	61.71	11.68	6.09	0.00467	1.6920	333.333
130	1.913	61.55	10.69	5.58	0.00460	2.2200	334.000
140	1.908	61.38	9.81	5.14	0.00454	2.8900	330.000
150	1.902	61.20	9.05	4.76	0.00447	3.7200	328.000
160	1.896	61.00	8.38	4.42	0.00441	4.7400	326.000
170	1.890	60.80	7.80	4.13	0.00434	5.9900	322.000
180	1.883	60.58	8.26	3.85	0.00427	7.5100	318.000
190	1.876	60.36	6.78	3.62	0.00420	9.3400	313.000
200	1.868	60.12	6.37	3.41	0.00413	11.5200	308.000
212	1.860	59.83	5.93	3.19	0.00404	14.6900	300.000
[latex]^{\circ } C[/latex]	[latex]kg/m^{3} [/latex]	[latex]KN/m^{3} [/latex]	[latex]N-sec/m^{2} [/latex]	[latex]10^{-6} m^{2} /sec[/latex]	[latex]N/m[/latex]	[latex]KN/m^{2} abs[/latex]	[latex]10^{6} KN/m^{2} [/latex]
0	999.8	9.805	0.001781	1.785	0.0756	0.6110	2.02
5	1000.0	9.807	0.001518	1.519	0.0749	0.872	2.06
10	999.7	9.804	0.001307	1.306	0.0742	1.230	2.10
15	999.1	9.798	0.001139	1.139	0.0735	1.710	2.14
20	998.2	9.789	0.001002	1.003	0.0725	2.340	2.18
25	997.0	9.777	0.000890	0.893	0.0720	3.170	2.22
30	995.7	9.765	0.000798	0.800	0.0712	4.240	2.25
40	992.2	9.731	0.000653	0.659	0.0696	7.380	2.28
50	988.0	9.690	0.000547	0.553	0.0697	12.330	2.29
60	983.2	9.642	0.000466	0.474	0.0662	19.920	2.28
70	977.8	9.589	0.000404	0.413	0.0644	31.160	2.25
80	971.8	9.530	0.000356	0.364	0.0626	47.340	2.20
90	965.3	9.467	0.000315	0.326	0.0608	70.100	2.14
100	958.4	9.399	0.000282	0.294	0.0589	101.330	2.07

Question 1.35: Water at 50^◦ C is lifted from a tank to a higher elevation ...

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