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where
differential operator
are binomial coefficients.
when h = 0
Substituting into the expansion for Taylor'S expression
and re-arranging gives the following.
Maclaurin's series is a special case of Taylor's series. If x = 0 and h is replaced by x, then Taylor's expansion becomes
Solve by direct integration
u = flow rate, L/s
V R = volume of tank, L
C O = inlet concentration, g/L
C = tank and outlet concentration, g/L
T = time, s.
Determine C as a function of time.
Step 1 A mass balance on tank
Mass in Mass out = Accumulation in tank
Step 2 Separate C and t and integrate
or
Step 3 Determine A using the boundary condition
t = 0, C = C i, therefore A = C i ? C O
Step 4. The final solution is
or
or
in which F(x) is a function of x only, and f(y) a function of y only.
The general solution is
Solve the differential
dividing by xy,
where the constant C1 = ln C
giving
The factor 1/xy used to multiply throughout to separate the variables xy is called an...
