Answer:
7.5 cm
Explanation:
In the figure we can see a sketch of the problem. We know that at the bottom of the U-shaped tube the pressure is equal in both branches. Defining [tex] \rho_A: [/tex] Ethyl alcohol density and [tex] \rho_G: [/tex] Glycerin density , we can write:
[tex] \rho_A\times g \times h_1 + \rho_G \times g \times h_2 = \rho_G \times g \times h_3 [/tex]
Simplifying:
[tex] \rho_A\times h_1 = \rho_G \times (h_3 - h_2) (1) [/tex]
On the other hand:
[tex] h_1 + h_2 = \Delta h + h_3 [/tex]
Rearranging:
[tex] h_1 - \Delta h = h_3 - h_2 (2) [/tex]
Replacing (2) in (1):
[tex] \rho_A\times h_1 = \rho_G \times (h_1 - \Delta h) [/tex]
Rearranging:
[tex] \frac{h_1 \times (\rho_A - \rho_G)}{- \rho_G} = \Delta h [/tex]
Data:
[tex] h_1 = 20 cm; \rho_A = 0.789 \frac{g}{cm^3}; \rho_G = 1.26 \frac{g}{cm^3} [/tex]
[tex] \frac{20 cm \times (0.789 - 1.26) \frac{g}{cm^3}}{- 1.26\frac{g}{cm^3}} = \Delta h [/tex]
[tex] 7.5 cm = \Delta h [/tex]
