Air at 100 kPa and 25°C flows in a horizontal duct of variable cross section. The water column in the manometer that measures the difference between two sections has a vertical displacement of 8 cm. If the velocity in the first section is low and the friction is negligible, determine the velocity at the second section. Also, if the manometer reading has a possible error of ±2 mm, conduct an error analysis to estimate the range of validity for the velocity found.

Solution to 99P

Step 1</p>

In this question, we need to find the velocity at the second section of the horizontal duct and we also need to do error analysis to estimate the range of validity for the computed velocity.

Step 2</p>

Using the Bernoulli’s equation,

Where=PRESSURE,

=VELOCITY,

=Height,

=density,

=acceleration due to gravity.

The heights of both the points given in the diagram is same thus

We are neglecting the pressure difference in the duct, but the pressure difference in the manometer is given by,

= density of water=1000kg/m3

=acceleration due to gravity

= height of water column

Now we have to find the density of air,

We know that the ideal gas equation is,

=pressure

= volume

=mass of air

= temperature=298 K

= gas constant for the air =

Thus using the equation of velocity,