Question

A beaker of height 30 cm is filled with water (Sw = 1) up to a height of 10 cm. Now oil (So = 0:9) is poured into the beaker till it is completely filled. At what distance (in cm) from the base will the pressure be one-third the pressure at the base of the beaker?

(a) 27.33

(b) 19.2

(c) 10.8

(d) 2.67

I got this question in final exam.

My question comes from Pressure Distribution in a Fluid topic in chapter Pressure and Its Measurement of Fluid Mechanics

Answer 1

Correct choice is (b) 19.2

Easiest explanation: Gauge pressure at the base of the beaker = So * 10^3 * 0.2 * g + Sw * 10^3 * 0.1 * g = 2550.6Pa. Let the required height be h m from the base.

If 0.1 ≤ h < 0.3,

800(0.3 – h)g = ^1⁄3 * 2550.6

Thus, h = 0.192 (in the range considered).

Even if there’s no need to check for the other range, it’s shown here for demonstration purpose.If

0 < h ≤ 0.1,

800 * 0.2 * g + 10^3 * (0.2 – h) * g = ^1⁄3 * 2550.6

Thus, h = 0.2733 (out of the range considered). Hence, the correct answer will be 19.2 cm.