Apiezometer and a pitot tube are tapped into a 4-cm-diameter horizontal water pipe, and the height of the water columns are measured to be 26 cm in the piezometer and 32 cm in the pitot tube (both measured from the top surface of the pipe). determine the velocity at the center of the pipe.

1.08m/s

Explanation:

To develop this problem it is necessary to resort to the concept developed by Bernoulli in his equations in which

describes the behavior of a fluid along a channel.

Bernoulli's equation is given by

Where,

Pressure at determinated point

density (water in this case)

Velocity at determinated point

g = Gravity acceleration

z = Pressure heads at determinated point.

We know that the problem is given in an horizontal line, then the pressure heads is zero.

And for definition we know that,

Where h means the heights of water column measured by the pitot tube at the top and the piezometer. Then replacing both pressure with the previous values we have:

Then replacing

At the end of the pipe the speed is zero, since there is stagnation then:

Re-arrange for =

Replacing the values where and we have,

Therefore the velocity at the centerline is 1.08m/s

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.