Flow Measurement Devices Questions and Answers

Answer: C

The discharge through a V-notch varies as \(H^{5/2}\).

For a triangular notch of included angle \(\theta\):

\[ \begin{aligned} Q &= \frac{8}{15} C_d \sqrt{2g} \\ &\quad \times \tan\frac{\theta}{2}\, H^{5/2} \end{aligned} \]

The extra power compared with a rectangular weir comes from the width of the flow growing with the head. \(H^{3/2}\) is the law for a rectangular notch or weir, and \(H^{1/2}\) is the law for an orifice, where velocity alone grows as \(\sqrt{H}\). Discharge proportional to H fits none of these devices.

Answer: A

The coefficient of the Pitot tube is C = 0.984.

First find the mean velocity from the discharge, then the centre velocity:

\[ \begin{aligned} Q &= 1365/60000 = 0.02275\ \text{m}^3/\text{s} \\ A &= \pi (0.1)^2 = 0.03142\ \text{m}^2 \\ V_m &= 0.02275/0.03142 = 0.724\ \text{m/s} \\ V_c &= 0.724/0.83 = 0.872\ \text{m/s} \end{aligned} \]

The Pitot tube gives \(V_c = C\sqrt{2gh}\) with \(h = 0.04\) m of water:

\[ \begin{aligned} \sqrt{2 \times 9.81 \times 0.04} &= 0.886 \\ C &= 0.872/0.886 = 0.984 \end{aligned} \]

Using the mean velocity instead of the centre velocity gives about 0.82, which is not offered; the other options match no step.

Answer: C

The discharge is \(Q = KCh^{1/2}\).

Applying Bernoulli's equation and continuity between the inlet and the throat gives the theoretical discharge:

\[ Q_{th} = \frac{a_1 a_2}{\sqrt{a_1^2 - a_2^2}} \sqrt{2gh} \]

Everything except \(\sqrt{h}\) is fixed for a given meter, so it is grouped as the meter constant C, and the discharge coefficient K allows for losses: \(Q = KC\sqrt{h}\). Discharge must grow as the square root of the head, so the forms with h to the first power, or with roots on K or C, are wrong.

Answer: C

The correct matching is (a)-(III), (b)-(IV), (c)-(II), (d)-(I).

• Venturimeter: a converging-diverging section; the pressure drop at the throat measures the flow (a-III).
• Orifice meter: a plate with a hole in it, inserted in the pipe (b-IV).
• Pitot tube: a tube bent at right angles, its open end facing the flow, to measure velocity (c-II).
• Manometer: a device for pressure measurement (d-I).

Only one option has the venturimeter against the converging-diverging section and the orifice meter against the hole in a plate; the option (a)-(III), (b)-(II) swaps the orifice meter and the Pitot tube.

Answer: A

A venturi meter is used for measuring the flow rate.

The venturi meter has a converging section, a throat and a gradually diverging section. The fluid speeds up and its pressure falls at the throat; the pressure difference between the inlet and the throat, read on a manometer, gives the discharge through Bernoulli's and the continuity equations, \(Q = C_{d} A_{1}A_{2}\sqrt{2gh}/\sqrt{A_{1}^{2} - A_{2}^{2}}\).

It does measure a pressure drop, but only as the means of finding the discharge, which is its purpose. Point velocity is measured with a pitot tube, and total head is not what the device is built to give.