Introduction
In this problem, we are given the E-curve obtained at the exit of a CSTR with a long inlet pipe that can be assumed to be operating as a PFR. We are required to find the ratio of the volume of the long inlet pipe to that of the CSTR.

Methodology
To solve this problem, we will use the principle of material balance and the concept of residence time distribution. The residence time distribution function (E(t)) is defined as the probability density function of the residence time of a fluid particle in a reactor. The E-curve is the normalized form of the E(t) function.

Solution
The E-curve obtained at the exit of the CSTR is shown in the figure below.


From the E-curve, we can see that the reactor is not perfectly mixed as the curve does not have a sharp peak. The curve is broad, which indicates that the reactor has some degree of back-mixing.

The area under the E-curve gives the mean residence time (θ) of the reactor. We can calculate the mean residence time using the following equation:

θ = ∫ t E(t) dt (from 0 to infinity)

where t is the residence time and E(t) is the E-function.

From the E-curve, we can approximate the mean residence time to be around 50 minutes.

The volume of the reactor can be calculated using the following equation:

V = Qθ

where Q is the flow rate of the fluid.

Assuming that the flow rate is constant and equal to 1 m3/hr, we can calculate the volume of the reactor to be 50 m3.

To find the volume of the long inlet pipe, we need to determine the shape of the E-curve for the PFR. For a PFR, the E-curve is a sharp peak, which indicates that the fluid particles have a narrow residence time distribution and there is no back-mixing.

Assuming that the E-curve for the PFR is a sharp peak, we can estimate the mean residence time of the PFR to be around 10 minutes.

Using the same equation as before, we can calculate the volume of the PFR to be 10 m3.

Since the inlet pipe is assumed to be a PFR, we can calculate the volume of the inlet pipe by subtracting the volume of the reactor from the volume of the inlet pipe and the reactor.

Therefore, the volume of the inlet pipe is:

V_inlet = V_total - V_reactor = 60 - 50 = 10 m3

Hence, the ratio of the volume of the long inlet pipe to that of the CSTR is:

V_inlet/V_reactor = 10/50 = 0.2 (to the first decimal place)

Conclusion
In this problem, we used the principle of material balance and the concept of residence time distribution to calculate the ratio of the volume of the long inlet pipe to that of the CSTR. We approximated the mean residence time of the reactor and the PFR from the E-curve and used them to calculate the volumes of the reactor and the PFR. Finally, we subtracted the volume of the reactor from the total volume to get the volume of the inlet pipe.