Question:
A liquid of density 750 kgm–3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1 = 1.2 × 10–2 m2 to \(A_2=\frac{A_1}{2}.\) The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is _____ × 10–3 m3s–1.
A liquid of density 750 kgm–3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1 = 1.2 × 10–2 m2 to \(A_2=\frac{A_1}{2}.\) The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is _____ × 10–3 m3s–1.
Updated On: Jul 8, 2024
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Correct Answer: 24
Solution and Explanation
Using Bernoulli’s equation
\(P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho 4v_2^2\)
\(P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho 4v_2^2\)
\(\frac{3}{2}\rho v^2 = P_1 - P_2\)
\(⇒\) \(v = \sqrt{\frac{2}{3\rho}(P_1 - P_2)}\)
\(=\) \(\sqrt{\frac{2 \times 4500}{3 \times 750}} = 2\) m/sec
So \(Q = A1v =\) 24 × 10–3 m3/sec
Answer is 24.
So \(Q = A1v =\) 24 × 10–3 m3/sec
Answer is 24.
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Concepts Used:
Pressure
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
- The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
- Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.