A VENTURI TUBE IS USED TO MEASURE THE WATER SPEED V IN A PIPE BY COMPARING THE WATER PRESSURE IN THE WIDE AND NARROW SECTIONS(CROSS-SECTIONAL AREAS A, A=A/4).FIND V IF THE DIFFERENCE IN MECURY LEVEL IS h=25mm.(THE DENSITY OF MERCURY IS =13600Kg/meter cube)
A2 = A1/4, so you know A1v1 = A2v2
A1v1 = A1/4v2, cancel out the A1's
v1 = 1/4 v2
v2^2 = 16v1^2 --- eqn 1
change in pressure = (rho)gh = 3332 N/m^2
3332 = 1/2(rho)(v2^2 - v1^2)
3332 = (1/2)(1000)(v2^2 - v1^2)
v2^2 = 6.664 + v1^2 --- eqn 2
16v1^2 = 6.664 + v1^2
v1 = 0.6665 m/s
.... I hope this is right.
To find the water speed (V) using the Venturi tube, we can make use of the Bernoulli's equation. Bernoulli's equation states that the total energy per unit volume of fluid is conserved between any two points along a streamline. In this case, we will consider two points - one in the wide section and the other in the narrow section of the Venturi tube.
Let's denote the pressure in the wide section as P1 and the pressure in the narrow section as P2. The density of water is denoted as ρ (typically around 1000 kg/m^3). The cross-sectional area of the wide section is denoted as A, and the cross-sectional area of the narrow section is denoted as A/4.
According to Bernoulli's equation, we have:
P1/ρ + V1^2/2 = P2/ρ + V2^2/2
Since the fluid is incompressible, the densities on both sides cancel out. Also, the initial velocity (V1) is generally very small compared to the velocity in the narrow section (V2). Therefore, we can assume V1 ≈ 0. The equation reduces to:
P1/ρ = P2/ρ + V2^2/2
Now, let's consider the pressure difference (ΔP = P1 - P2) in terms of the height difference of mercury (h):
ΔP = ρgh
where g is the acceleration due to gravity. In this case, we have:
ΔP = ρgh = (13600 kg/m^3) * (9.8 m/s^2) * 25 mm * (1 m/1000 mm)
Note that we've converted the height difference from millimeters to meters.
Now, to find V2, let's rearrange the equation:
V2^2/2 = ΔP
V2 = sqrt(2 * ΔP)
Substituting the value of ΔP, we have:
V2 = sqrt(2 * (13600 kg/m^3) * (9.8 m/s^2) * 25 mm * (1 m/1000 mm))
Simplifying the calculation inside the square root:
V2 = sqrt(2 * (13600 kg/m^3) * (9.8 m/s^2) * 25 * 0.001)
V2 ≈ 23.45 m/s
Therefore, the water speed (V) in the pipe is approximately 23.45 m/s.