Saturated Water Properties

M.M. Yovanovich

WATERPROPS1.MWS

Correlation equation for saturated water properties from 0 to 100 degrees C.

> restart:

> water0:= (k=0.552, rho=1002.28, cp=4217.8, nu=1.788e-6, alpha=1.308e-7, Pr=13.6);

> water20:= (k=0.597, rho=100.52, cp=4181.8, nu=1.006e-6, alpha=1.430e-7, Pr=7.02);

> water40:= (k=0.628, rho=994.59, cp=4178.4, nu=0.658e-6, alpha=1.512e-7, Pr=4.34);

> water60:= (k=0.651, rho=985.46, cp=4184.3, nu=0.478e-6, alpha=1.554e-7, Pr=3.02);

> water80:= (k=0.668, rho=974.08, cp=4196.4, nu=0.364e-6, alpha=1.636e-7, Pr=2.22);

> water100:= (k=0.680, rho=960.63, cp=4216.1, nu=0.294e-6, alpha=1.680e-7, Pr=1.74);

Temperature and property value pairs.

> kvals:=
[[0, op(2,water0[1])],
[20, op(2,water20[1])],
[40, op(2,water40[1])],
[60, op(2,water60[1])],
[80, op(2,water80[1])],
[100, op(2,water100[1])]];

> rhovals:=
[[0, op(2,water0[2])],
[20, op(2,water20[2])],
[40, op(2,water40[2])],
[60, op(2,water60[2])],
[80, op(2,water80[2])],
[100, op(2,water100[2])]];

> cpvals:=
[[0, op(2,water0[3])],
[20, op(2,water20[3])],
[40, op(2,water40[3])],
[60, op(2,water60[3])],
[80, op(2,water80[3])],
[100, op(2,water100[3])]];

> nuvals:=
[[0, op(2,water0[4])],
[20, op(2,water20[4])],
[40, op(2,water40[4])],
[60, op(2,water60[4])],
[80, op(2,water80[4])],
[100, op(2,water100[4])]];

> alphavals:=
[[0, op(2,water0[5])],
[20, op(2,water20[5])],
[40, op(2,water40[5])],
[60, op(2,water60[5])],
[80, op(2,water80[5])],
[100, op(2,water100[5])]];

> Prvals:=
[[0, op(2,water0[6])],
[20, op(2,water20[6])],
[40, op(2,water40[6])],
[60, op(2,water60[6])],
[80, op(2,water80[6])],
[100, op(2,water100[6])]];

Correlation equations.

> with(stats):

> temps:= [0,20,40,60,80,100]:

> fit[leastsquare[[T,k], k=a*T^2+b*T+c, {a,b,c}]]([
temps, [.552,.597, .628, .651, .668, .680]]);

> k:= T->-.9866071429e-5*T^2+.2238035714e-2*T+.5536071429;

> fit[leastsquare[[T,rho], rho=a*T^2+b*T+c, {a,b,c}]]([
temps, [1002.28, 1000.52, 994.59, 985.46, 974.08, 960.63]
]);

> rho:= T->-.3582589286e-2*T^2-.6559821429e-1*T+1002.676071;

> fit[leastsquare[[T,cp], cp=a*T^3+b*T^2+c*T+d, {a,b,c,d}]]([
temps,
[4217.8, 4181.8, 4178.4, 4184.3, 4196.4, 4216.1]]);

> cp:=T->-.1554398148e-3*T^3+.3851686508e-1*T^2-2.313042328*T+4216.855556;

> fit[leastsquare[[T,nu], nu=a*T^4+b*T^3+c*T^2+d*T+e, {a,b,c,d,e}]]([
temps, [.1788e-5, .1006e-5, .658e-6, .478e-6, .364e-6, .294e-6]
]);

> nu:=T->.3177083333e-13*T^4-.8965277778e-11*T^3+.9827083333e-9*T^2-.5532222222e-7*T+.1787666667e-5;

> fit[leastsquare[[T,alpha], alpha=a*T^4+b*T^3+c*T^2+d*T+e, {a,b,c,d,e}]]([
temps, [.1308e-6, .1430e-6, .1512e-6, .1554e-6, .1636e-6, .1680e-6]
]);

> alpha:= T->-.1015625000e-14*T^4+.2320601852e-12*T^3-.1855902778e-10*T^2+.9248148148e-9*T+.1307055556e-6;

> fit[leastsquare[[T,Pr], Pr=a*T^4+b*T^3+c*T^2+d*T+e, {a,b,c,d,e}]]([
temps, [13.6, 7.02, 4.34, 3.02, 2.22, 1.74]
]);

> Pr:= T-> .3046875000e-6*T^4-.8457175926e-4*T^3+.8985763889e-2*T^2-.4760621693*T+13.59579365;

> T1:= 50:

> waterprops1:= evalf([k=k(T1), rho=rho(T1), cp=cp(T1), nu=nu(T1), alpha=alpha(T1), Pr=Pr(T1)],4);

>