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)
To find the water speed (V), we can use Bernoulli's equation which relates the pressure, density, and velocity of an ideal fluid flowing through a Venturi tube. Bernoulli's equation is given as:
P1 + (1/2) * rho * V1^2 = P2 + (1/2) * rho * V2^2
Where:
P1 and P2 are the pressures at the wide and narrow sections of the Venturi tube, respectively.
V1 and V2 are the velocities of the water at the wide and narrow sections of the Venturi tube, respectively.
rho is the density of the fluid.
In this case, the wide section has a cross-sectional area of A, and the narrow section has a cross-sectional area of A/4.
Let's assume P1 and P2 are the atmospheric pressures (since they were not given), which we can consider as zero gauge pressure. Therefore, the equation can be simplified to just focusing on velocity:
(1/2) * rho * V1^2 = (1/2) * rho * V2^2
Since the density of water remains constant, we can cancel it out:
V1^2 = V2^2
The difference in mercury level (h) can be used to find the difference in velocity (delta V) between the wide and narrow sections:
delta V = V1 - V2
We can use the equation of hydrostatic pressure to determine the difference in pressure (delta P) between the wide and narrow sections:
delta P = rho * g * h
Where:
g is the acceleration due to gravity.
Since the fluid is incompressible (water), the pressure difference is due to the change in kinetic energy:
delta P = (1/2) * rho * (V1^2 - V2^2)
We know that V1^2 = V2^2, so we have:
delta P = 0
Therefore, there is no change in pressure between the wide and narrow sections of the Venturi tube. This implies that the difference in mercury level (h) does not affect the velocity (V) of the water flowing through the Venturi tube.
Hence, we cannot determine the water speed (V) based on the given information. Additional data or equations are required to solve for V.