GATE 2019 BT Q.42: solution and answer

GATE 2019 · BTQ.42 · 2 marks · MCQ

Match the instruments in Group I with their corresponding measurements in Group II.

| Group I | Group II |
|---|---|
| P. Manometer | 1. Agitator speed |
| Q. Rotameter | 2. Pressure difference |
| R. Tachometer | 3. Cell number |
| S. Haemocytometer | 4. Air flow rate |

(A)
P-4, Q-1, R-2, S-3
(B)
P-3, Q-4, R-1, S-2
(C)
P-2, Q-4, R-1, S-3
(D)
P-2, Q-1, R-4, S-3

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Answer and solution

ANSWER

(C) P-2, Q-4, R-1, S-3. A manometer reads a pressure difference, a rotameter reads the air flow rate, a tachometer reads the agitator speed and a haemocytometer gives the cell number.

Official answer: CSource: Official answer key, GATE 2019 BT (IIT Madras)

P, Manometer: a U-tube partly filled with a liquid of density $ρ_{m}$ . The two limbs are connected to two points in the line, and the difference $h$ between the liquid levels gives the pressure difference between them, $Δ P = (ρ_{m} - ρ) g h$ , where $ρ$ is the density of the fluid above the manometer liquid. For a gas, $ρ ≪ ρ_{m}$ , so $Δ P \approx ρ_{m} g h$ . So P-2.
Q, Rotameter: a variable-area flow meter. A float rises in a tapered, vertical glass tube until drag and buoyancy balance its weight, and the height of the float gives the volumetric flow rate. On a fermenter it is the standard meter for the air (gas) flow into the sparger. So Q-4.
R, Tachometer: measures rotational speed, in $rpm$ . On a bioreactor that is the speed of the agitator (impeller) shaft. So R-1.
S, Haemocytometer: a counting chamber of known depth with an etched grid. The cells in a known volume are counted under the microscope, which gives the cell number (cell concentration). So S-3.
Matching: P-2, Q-4, R-1, S-3. Only option (C) has this. Each of the other options breaks at least one pair: (A) puts the manometer on air flow rate, (B) puts the manometer on cell number and the haemocytometer on pressure difference, and (D) swaps the rotameter and the tachometer.

KEY IDEA

Match each instrument to the physical quantity it senses. A manometer reads a liquid-column height, so it gives a pressure difference. A rotameter reads the height of a float in a tapered tube, so it gives a flow rate (on a fermenter, the air flow to the sparger). A tachometer reads the speed of a rotating shaft (the agitator). A haemocytometer is a counting chamber of known volume, so it gives the cell number.

WATCH OUT FOR

Mixing up the rotameter and the tachometer because both names suggest rotation, which leads to option (D). The rotameter's float spins, but what it measures is flow rate. The tachometer is the instrument that measures rotational speed (rpm).

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GATE 2019 BT Q.42: solution and answer

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