This set of Process Control Multiple Choice Questions & Answers (MCQs) focuses on “Examples of First-Order Systems”.

1. Which of the following resistance has linear relationship between flow and head?

a) A linear resistance

b) Sinusoidal resistance

c) Ramp resistance

d) Step resistance

View Answer

Explanation: Let’s take the example of a linear system like the liquid level system. In that, resistance R = \(\frac {H}{q}\), where H is the height of the liquid and q is the volumetric flow rate of the liquid. Here, it can be seen that the resistance has a linear relationship between flow and the head.

2. Which of the following options is correct time constant for liquid level system?

a) h / mc_{p}

b) mc_{p} / h

c) 1 / AR

d) AR

View Answer

Explanation: For a liquid level tank system,

After converting the basic mass balance equation to deviation variables and in laplace domain,

Q(s) = \(\frac {1}{R}\) H(s) + AsH(s)

Or, Q(s) / H(s) = \(\frac {1}{R}\) + As

Or, Q(s) / H(s) = \(\frac {1 + ARs}{R}\)

Or, H(s) / Q(s) = \(\frac {R}{1 + ARs}\)

Hence here the time constant is T = AR.

3. Which of the following options is correct time constant for mixing system, where V is the volume of the mixing liquid and q is the volumetric flow?

a) V / q

b) V × q

c) q / V

d) 1 / V

View Answer

Explanation: We know that for mixing system,

qX(t) – qY(t) = V\(\frac {dY}{dt}\)

Taking laplace,

qX(s) – qY(s) = V[Y(s)]

Y(s) / X(s) = \(\frac {1}{\frac {V}{q} + 1}\)

Here the time constant is T = V / q

4. Which of the following options is correct time constant for heating system?

a) W / pV

b) pVW

c) W / pV

d) pV / W

View Answer

Explanation: For a heating system,

– wCT + Q = pVC\(\frac {dT}{dt}\)

Taking laplace transform and rearranging into T(s) / Q(s) form we get,

\(\frac {T(s)}{Q(s)} = \frac {1 / WC}{(\frac {pV}{W})s + 1}\)

Hence, here T = pV / W

5. Which of the following options correctly represent the series used for linearization of non linear system?

a) Taylor series

b) Stanford series

c) Fourier series

d) Hunan series

View Answer

Explanation: A nonlinear system can be transformed into a linear transfer function by taylor series. In general, this technique may be applied to any nonlinearity that can be expressed in a Taylor series (or, equivalently, has a unique slope at the operating point). Since this includes most nonlinearities arising in process control, we have ample justification for studying linear systems in considerable detail.

6. Which of the following statement is correct for interacting and non – interacting systems?

a) A noninteracting system of tanks affects the liquid level of both the tanks due the change in liquid output of one of the tanks

b) A noninteracting system of tanks does not affect the liquid level of the first tanks due the change in liquid output of the second tank

c) An interacting system of tanks affects the liquid level of the first tank due the change in liquid output of one of the tanks

d) An interacting system of tanks affects the liquid level of the second tank due the change in liquid output of one of the tanks

View Answer

Explanation: Since the two tanks are not interacting with each other, any change in output of the second tank will not affect the liquid level of the first tank. Hence, in a noninteracting system of tanks, due to the change in liquid output of the second tank, the liquid level of the first tanks is not affected.

7. Which of the following statement is correct for interacting and non – interacting systems?

a) A noninteracting system of tanks affects the liquid level of both the tanks due the change in liquid output of one of the tanks

b) A noninteracting system of tanks affects the concentration of the first tanks due the change in liquid output of the second tank

c) In an interacting system of tanks, the liquid level of the first tank changes due to a change in the output of the second tank.

d) An interacting system of tanks affects the concentration of the second tank and first tank due the change in liquid output of one of the tanks

View Answer

Explanation: Since the two tanks are interacting with each other, any change in output of the second tank will affect the liquid level of the first tank. Hence, in a interacting system of tanks, due to the change in liquid output of the second tank, the liquid level of the first tanks is affected.

8. A mixing tank is having flow rate of 10 LPM. The volume of the tank is 100L. What is the time constant in seconds?

a) 10

b) 1

c) 100

d) 0.1

View Answer

Explanation: For a mixing tank, time constant T = V / q, V is the volume of the tank and q is the volumetric flow rate. So as per the given data, T = 100 / 10 i.e. 10s.

9. A liquid level tank is having resistance of 20 unit and a cross sectional area of 0.2 m^{2}. What is the time constant?

a) 4s

b) 40s

c) 0.01s

d) 0.631s

View Answer

Explanation: For a liquid level system, time constant T = A × R, A = cross sectional area and R is the resistance.

So, T = 0.2 × 20 = 4s.

10. Which of the following is correct regarding first order mixing process?

a) Agitator is used for uniform mixing and heat transfer

b) Jacket is used for adiabatic operation

c) Agitator use hampers heat transfer rate

d) Jacket is used for isobaric operation

View Answer

Explanation: In order to maintain a homogeneous system, agitator is used for proper mixing and proper heat transfer rate.

**Sanfoundry Global Education & Learning Series – Process Control.**

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