three different liquids are used in a manometer.
(a) derive an expression for P1-P2 in terms of ro(a), ro(b), ro(c), h1, and h2
(b) suppose fluid A is methanol, B is water, and C is a manometer fluid with a specific gravity of 1.37; pressure P2=121.0 kPa; h1=24.0 cm. Calculate P1(kPa).
P1-P2=ro(b)+ro(c)-ro(a)
P1=121.0kPa+[(1.00g/cm3)(980.7cm/s2)(30.0cm)(1dynes/1gcm/s2)]+[(1.37g/cm3)(980.7cm/s2)(24.0cm)(1dynes/1gcm/s2)]-[(.792g/cm3)(980.7cm/s2)(54.0cm)(1dynes/1gcm/s2)]
P1=121.0kPa+(2.94kPa+3.22kPa-4.19kPa)
P1=121.0kPa+1.97kPa
P1=123.0kPa
I think this is right, I just did it for homework.
I got the same answer
Suppose fluid A is methanol, B is water, and C is a manometer fluid with a
specific gravity of 1.37; pressure P2 = 121.0 kPa; h1 = 33.0 cm, and h2 = 25.0
cm. Calculate P1 (kPa).
To derive an expression for P1-P2 in terms of the densities (ro) and heights (h) of the three different liquids (A, B, and C), we need to consider the pressure differences at each liquid interface. Let's go step by step:
(a) Deriving an expression for P1-P2:
Assuming fluid A is above fluid B, and fluid B is above fluid C in the manometer, we can start by considering the pressure difference between fluid A and fluid B (P1a).
At any point in the manometer, the pressure difference between two adjacent fluids is given by the hydrostatic pressure equation:
ΔP = Δh * ro * g
Here, ΔP is the pressure difference, Δh is the difference in height between the two fluids, ro is the density of the fluid, and g is the acceleration due to gravity.
So, the pressure difference between fluid A and fluid B (P1a) is:
P1a = h1 * ro(a) * g
Similarly, we can consider the pressure difference between fluid B and fluid C (P1b):
P1b = h2 * ro(b) * g
Finally, the total pressure difference (P1-P2) between fluid A and the manometer fluid C can be obtained by adding P1a and P1b together:
P1 - P2 = P1a + P1b
P1 - P2 = h1 * ro(a) * g + h2 * ro(b) * g
Hence, the expression for P1-P2 in terms of the densities (ro(a), ro(b)) and heights (h1, h2) is:
P1 - P2 = g * (h1 * ro(a) + h2 * ro(b))
(b) Calculating P1:
Given: P2 = 121.0 kPa, h1 = 24.0 cm
We are also given the specific gravity of fluid C, which is 1.37. Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). Therefore, the density of fluid C (ro(c)) can be determined as:
ro(c) = ro(b) * specific gravity of C
ro(c) = ro(b) * 1.37
Substituting the values into the derived expression, we can calculate P1:
P1 - 121.0 kPa = 9.81 m/s^2 * (24.0 cm * ro(a) + h2 * ro(b))
P1 = 121.0 kPa + 9.81 m/s^2 * (24.0 cm * ro(a) + h2 * ro(b))
You will need the values of the densities (ro(a), ro(b)), the specific gravity of fluid C, and the value of h2 in order to calculate P1.