### BRAVO! That is the right answer.

We will apply Bernoulli's Equation
(1/2) 1 v12 + P1 + 1 g y1 = (1/2) 2 v22 + P2 + 2 g y2

to the two regions. Since they are at the same height, the two y-terms are the same and we have only

(1/2) 1 v12 + P1 = (1/2) 2 v22 + P2

The density is the same in both regions so we have

(1/2) v12 + P1 = (1/2) v22 + P2

As we did in the previous Q&A Example, we can change the subscripts to "n" and "W" for the "narrow" and "Wide" regions; then Bernoulli's Equation is

(1/2) vn2 + Pn = (1/2) vW2 + PW

and we know everything in this equation except Pn,

Pn = (1/2) vW2 + PW - (1/2) vn2

Pn = PW + (1/2) vW2 - (1/2) vn2

Pn = PW + (1/2) [ vW2 - vn2 ]

Pn = 15 mmHg + (1/2) [ 1000 kg/m3] [ (2.5 m/s)2 - (6.2 m/s)2 ]

Pn = 15 mmHg + (1/2) [ 1000 kg/m3] [ (6.25 m2/s2) - (38.44 m2/s2) ]

Pn = 15 mmHg + (1/2) [ 1000 kg/m3] [ - 32.19 m2/s2 ]

Pn = 15 mmHg - (1/2) (1000 kg/m3)(32.19 m2/s2)

Before we go on, notice that the pressure is going to be less in the narrow region. And that is just as we would/should expect since the velocity is greater there!

Pn = 15 mmHg - (1/2) (32,190 (kg m/s2) / m2

Pn = 15 mmHg - 16,095 N / m2

Pn = 15 mmHg - 16,095 Pa

Remember, you can't add apples and oranges! What about terms in mmHg and in Pa. Those both measure pressure but we have to convert one of them. Since we started with a pressure of 15 mmHg in the wide region, let's stay with units of mmHg and convert the term with units of Pa,

16.095 kPa = 16,095 Pa [ 1 mmHg / 133 Pa ] = 121 mmHg

Pn = 15 mmHg - 121 mmHg

Pn = - 106 mmHg

What does this negative pressure mean? Both PW and Pn are gauge pressures. When we state

Pw = 15 mmHg

that means the pressure in the wide region is 15 mmHg greater than atmospheric pressure. Now that we have calculated

Pn = - 106 mmHg

that means the pressure in the narrow regions is 106 mmHg less than atmospheric pressure. That means the U-tube manometers would look something like this --

or