A closed manometer is filled with an oil with density of 0.776 g/mL. What is the pressure in mmHg when the liquid column in the manometer stands at 85.7 mm?

im not sure what mm is suppose to stand for here (probably meters but that doesnt fit into the formulas ive been taught)

i know the answer is 4.89mmHg but can someone tell me how you solve this??
thank you very much

mm stands for millimeters.

density x height = pressure but if you want it in units of mm Hg you must divide by density of Hg.
0.776 x 85.7/13.59 = ?

DrBob thanks for the answer but where did u get 13.59???

also how do the units cross out to end up with mmHg?

13.59 is the density of Hg.

Here is a VERY good site you can read AND you can plug in your numbers and read the answer in kPa, atm, mm Hg, inches/water, lbs/sq ft etc.
http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html
Plugging numbers into the site calcn you should get this,
0.776g/cc x 0.0857m x 9.80 m/s = 0.6517 kPa. Divide by 101.325 to convert to atm, multiply by 760 to convert to mm Hg. 0.6517*760/101.325 = 4.888 mm Hg which rounds to 4.89 mm Hg. (Note: The 13.59 is built into the last conversion factors of 760 and 101.325).

Another note: I would go with the second calcn (as in the site I posted) since my short cut I used in the first response doesn't give this exact answer.

To solve the problem, you can use the concept of pressure in a fluid and apply the hydrostatic pressure formula. The formula is given by:

P = ρgh

where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the liquid column.

In this case, the fluid is oil and its density is given as 0.776 g/mL. To use the formula, you need to convert the density from g/mL to g/cm³. Since 1 mL is equal to 1 cm³, the density remains the same. So, ρ = 0.776 g/cm³.

The height of the liquid column, h, is given as 85.7 mm. However, to use the formula, you need to convert it to centimeters (cm) since the density is in g/cm³. Since 1 mm is equal to 0.1 cm, the height becomes h = 85.7 mm × 0.1 cm/mm = 8.57 cm.

The acceleration due to gravity, g, is approximately 9.8 m/s².

Now, you can substitute the values into the formula:

P = ρgh
P = 0.776 g/cm³ × 9.8 m/s² × 8.57 cm

Notice that the units cancel out in the calculation, leaving only mmHg as the unit for pressure. Evaluating the expression:

P ≈ 4.89 mmHg

Therefore, the pressure in the closed manometer is approximately 4.89 mmHg.