Mechanical Properties of Fluids

Topics in this chapter

• Pressure, Buoyancy And Manometers
• Fluid Flow And Bernoulli Principle
• Viscosity And Terminal Velocity
• Surface Tension And Capillarity

Cheat sheet

Practice questions

1. Question 1Q-2D1DAE

   A U-tube of uniform cross-section contains mercury. Water is poured into one limb until a column of height 13.6 cm is formed. Above the water in that limb, oil of density $0.8 \text{ g/cm}^3$ is poured until the top surfaces of oil and mercury in the other limb are at the same horizontal level. If the height of the oil column is $h$, find $h$ given that the density of mercury is $13.6 \text{ g/cm}^3$.

   1. A.12.0 cm
   2. B.13.6 cm
   3. C.15.0 cm
   4. D.10.0 cm
   See the answer and solution
2. Question 2Q-8EEF26

   A small spherical ball of radius $r$ and density $\rho$ falls freely under gravity through a height $h$ before entering a tank of water (density $\sigma$, viscosity $\eta$). If the ball does not lose any kinetic energy upon entering the water, the maximum depth to which it sinks inside the water is given by (neglect buoyant force during entry, assume terminal velocity is not reached quickly):

   1. A.$\frac{h(\rho - \sigma)}{\sigma}$
   2. B.$\frac{h\rho}{\sigma - \rho}$
   3. C.$\frac{h\rho}{\rho - \sigma}$
   4. D.$\frac{h(\rho - \sigma)}{\rho}$
   See the answer and solution
3. Question 3Q-02E130

   Two soap bubbles of radii $r_1$ and $r_2$ ($r_1 < r_2$) coalesce isothermally in vacuum to form a single soap bubble of radius $r$. What is the correct relation between $r$, $r_1$, and $r_2$?

   1. A.$r = r_1 + r_2$
   2. B.$r = \sqrt{r_1^2 + r_2^2}$
   3. C.$r = \sqrt[3]{r_1^3 + r_2^3}$
   4. D.$r = \frac{r_1 r_2}{r_1 + r_2}$
   See the answer and solution
4. Question 4Q-5849F6

   Water flows through a horizontal pipe whose internal diameter changes from 4 cm at one end to 2 cm at the other end. If the speed of water at the wider end is $2\text{ m/s}$, the speed of water at the narrower end is:

   1. A.$2\text{ m/s}$
   2. B.$4\text{ m/s}$
   3. C.$8\text{ m/s}$
   4. D.$16\text{ m/s}$
   See the answer and solution
5. Question 5Q-D03898

   A cylindrical vessel filled with liquid is rotated about its vertical axis of symmetry with a constant angular velocity $\omega$. The shape of the free surface of the liquid is a:

   1. A.Hemisphere
   2. B.Cone
   3. C.Paraboloid of revolution
   4. D.Hyperboloid
   See the answer and solution