4. Suppose that the initial salt concentration in the pipe with sealed ends is given by P(x,0)=(Q/(AH), for (L-H)/2 < x < (L + H)/2, elsewhere. The salt is deposited in the middle over a region of length H < L. The cross-sectional area is A. Show that the total amount of salt deposited is Q. Find the Fourier coefficients in the solution (4.1.36). Plot the results for the choices D/L = 1 per sec, and H/L = 1/2, 1/4, 1/8 at times t = 0.01,0.1 sec: you need only consider the first three terms in the Fourier series for the solution. What do you observe happening? Can you take the limit as H 0; this describes the deposit of a point source at L/2. What does the solution look like at t = 0.01, 0.1? Compare it to the sequence in H.