Physics · Mechanical Properties Of Fluids · NEET
It directly reads a pressure difference between the wide pipe and the narrow throat, but its real purpose is to find the speed (and volume flow rate) of the fluid. The manometer shows a height difference h that comes from the pressure drop. We then use the formula to convert that pressure drop into velocity. So the measured thing is pressure difference, the wanted answer is speed.
By the equation of continuity, A1 v1 = A2 v2. A smaller area A2 forces a larger speed v2. By Bernoulli's principle, along a horizontal pipe, P + half rho v squared = constant. When v goes up, P must go down to keep the sum constant. So the narrow throat has high speed and low pressure. This is the whole idea behind the venturimeter.
It works on Bernoulli's principle (energy conservation in flowing fluid) combined with the equation of continuity (Av = constant). Bernoulli links speed to pressure, and continuity links the two pipe areas to the two speeds. Together they give the working formula. It does NOT use Pascal's law or Archimedes' principle.
For a horizontal pipe, Bernoulli gives P1 + half rho v1 squared = P2 + half rho v2 squared. Continuity gives v2 = (A1/A2) v1. The manometer gives the pressure difference P1 minus P2 = rho_m g h (with rho_m the manometer liquid density). Substitute and solve for v1: v1 = A2 times square root of (2 (P1 - P2) divided by (rho (A1 squared minus A2 squared))). Flow rate Q = A1 v1.
A venturimeter measures the average flow speed inside a pipe using a narrow throat and the pressure drop there. A pitot tube measures the speed of flow at one point by comparing static pressure and stagnation pressure (where the fluid is brought to rest). Both use Bernoulli's principle, but the venturimeter uses a constriction while the pitot tube uses a stopped stream.
When the pipe is horizontal, the height h1 equals h2, so the rho g h terms in Bernoulli's equation cancel out. That leaves only the pressure and speed terms, which makes the maths simple. If the pipe were tilted, you would also need to include the height difference. NEET problems almost always use the horizontal case.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is used to measure the speed of a fluid and the volume flow rate through a pipe, for example water or oil in industrial pipelines.
It works on Bernoulli's principle together with the equation of continuity. Faster flow in the throat means lower pressure, and that pressure drop gives the speed.
v1 = A2 times square root of [2(P1 - P2) / (rho (A1 squared - A2 squared))], where P1 - P2 = rho_m g h from the manometer. Flow rate Q = A1 v1.
At the narrow throat, because the fluid moves fastest there. High speed means low pressure by Bernoulli's principle.
No. A venturimeter uses a narrow throat and a pressure drop to find average flow speed; a pitot tube compares static and stagnation pressure at a point. Both rely on Bernoulli's principle.
