The Venturi meter is used to measure the speed of air (density rho_a and is show

Question

The Venturi meter is used to measure the speed of air (density rho_a and is shown in the figure below. It consists of a horizontal pipe with variable sectional areas, and a flexible hose, partially filled with water (density rho_w), connecting two points in the pipe with different areas. Air enters the meter at speed v_i and atmospheric pressure p_0. The sectional area of the meter is A_1 at point 1 and A_2 at point 2. What is the speed of the air at point 2? What is the pressure of the air at point 2? What is the value of h, the difference between the water levels at 3 and 4? If the speed v_1 doubles, how much bigger (or smaller does h become? Notice that h is not a given parameter of the problem.

Explanation / Answer

part a:

as flow rate remains the same,

A1*v1=A2*v2

hence speed of air at 2=v2=A1*v1/A2

part b:

using bernoulli's equation:

P1+pho*g*h1+0.5*pho*v1^2=P2+pho*g*h2+0.5*pho*v2^2

here h1=h2

so corresponding terms will cancel each other.

P1=atmospheric pressure=p0

then P2=P1+0.5*pho*(v1^2-v2^2)

=p0+0.5*pho*(v1^2-(A1*v1/A2)^2)

part c:

as pressure at point 3 is same as point 1=p0

pressure at point 4 is same as point 2.

and noting that P3+pho*g*h=P4

==>p0+pho*g*h=P2

==>h=(P2-p0)/(pho*g)

==>h=0.5*pho*(v1^2-(A1*v1/A2)^2)/(pho*g)

==>h=0.5*(v1^2-(A1*v1/A2)^2)/g

part d:

from part c,

h=0.5*v1^2*(1-(A1/A2)^2)/g

as h is directly proportional to square of v1,

if v1 is doubled, h will become 2^2=4 times

so h will be 4 times higher as compared to previous value.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.