A horizontal venturimeter is used to measure the flow speed of water (density = 1000 kg m^ -3 ). The cross-sectional areas of the wide and narrow sections of the pipe are 30 cm^2 and 10 cm^2 , respectively. A U-tube

Question

Quantrex Academy · Accepted Answer

Correct answer: C. 2 m s^ -1

Let the flow speed at the wide section be

v_1

and at the narrow section be

v_2

.

From the equation of continuity:

A_1 v_1 = A_2 v_2

30 \times v_1 = 10 \times v_2 \Rightarrow v_2 = 3 v_1

The pressure difference

\Delta P

between the two sections is given by the manometer reading:

\Delta P = (\rho_m - \rho_w) g h

Substitute the given values (

\rho_m = 5000 \text{ kg m}^{-3}

,

\rho_w = 1000 \text{ kg m}^{-3}

,

h = 0.4 \text{ m}

):

\Delta P = (5000 - 1000) \times 10 \times 0.4 = 4000 \times 4 = 16000 \text{ Pa}

Applying Bernoulli's equation for a horizontal pipe:

\Delta P = \dfrac{1}{2} \rho_w (v_2^2 - v_1^2)

16000 = \dfrac{1}{2} \times 1000 \times ((3 v_1)^2 - v_1^2)

16000 = 500 \times (9 v_1^2 - v_1^2)

16000 = 500 \times 8 v_1^2

16000 = 4000 v_1^2

v_1^2 = 4 \Rightarrow v_1 = 2 \text{ m s}^{-1}

Answer:

2 \text{ m s}^{-1}

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