Discussion
The pressure drop through a well-designed constriction is to be used for measuring the velocity of flow through a circular pipe. If the pressure drop from a 0.1 m diameter section to a 0.05 m diameter section of the pipe is 7.5 kPa, the velocity in m s-1 in the 0.1 m diameter section of the pipe is ____________.
(Take density of liquid = 1000 kg m-3)
Answer: B
The velocity in the 0.1 m section is 1.0 m/s.
The constriction acts as a venturi meter. Continuity links the two velocities: the diameter halves, so the area falls to a quarter and \(V_{2} = 4V_{1}\). Bernoulli’s equation between the two sections then gives
\[ \begin{aligned} \Delta p &= \tfrac{1}{2}\rho(V_{2}^{2} - V_{1}^{2}) = \tfrac{1}{2}\rho(16 - 1)V_{1}^{2} \\ 7500 &= 500 \times 15 V_{1}^{2} \\ V_{1} &= 1.0\ \text{m/s} \end{aligned} \]
The throat velocity is 4.0 m/s. A value of 0.5 or 1.5 would give pressure drops of 1.9 kPa or 16.9 kPa, and 2.0 m/s would need 30 kPa.
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