Mechanical Properties of Fluids — MHT-CET Physics

Formulas (2)

• Pressure with Depth, and the Rising Bubble · Rising bubble
  $$(P_0 + \rho g d)\,V_1 = P_0\,V_2 \;\Rightarrow\; \rho g d = P_0\left(\frac{V_2}{V_1} - 1\right)$$
• Upthrust, and How Deep a Light Body Sinks · Maximum depth
  $$d_{\max} = \frac{2gh}{2\,(\sigma - \rho)g/\rho} = \frac{h\rho}{\sigma - \rho}$$

Watch out for (2)

• Using 8H instead of 7H
  → Pressure with Depth, and the Rising Bubble
• Writing the deceleration as (σ − ρ)g
  → Upthrust, and How Deep a Light Body Sinks

Formulas (3)

• Surface Tension as a Force Along a Line · Film between two plates
  $$F = \frac{2TA}{t} = \frac{2TA^2}{V}$$
• Work on Films and Soap Bubbles · Soap bubble
  $$W = 2 \times 4\pi R^2\,T = 8\pi R^2 T$$
• Drops that Split or Merge · Splitting a drop
  $$W = 4\pi R^2 T\left(n^{1/3} - 1\right), \qquad \frac{E_{\text{droplets}}}{E_{\text{drop}}} = n^{1/3}$$

Reference tables (1)

Watch out for (4)

• Counting only the outer rim of a ring
  → Surface Tension as a Force Along a Line
• Forgetting the second surface
  → Work on Films and Soap Bubbles
• Using n^(2/3) for the total surface
  → Drops that Split or Merge
• Thinking surface molecules have LESS energy
  → Surface Molecules, Temperature and Impurities

Formulas (2)

• Excess Pressure Inside a Drop and a Bubble · Excess pressure
  $$\Delta P_{\text{drop}} = \frac{2T}{r}, \qquad \Delta P_{\text{bubble}} = \frac{4T}{r}$$
• Capillary Rise · Capillary rise
  $$h = \frac{2T\cos\theta}{r\rho g}$$

Watch out for (3)

• Taking 1.01 : 1.02 as the pressure ratio
  → Excess Pressure Inside a Drop and a Bubble
• Using 2T/r for a soap bubble
  → Excess Pressure Inside a Drop and a Bubble
• Thinking the narrow tube holds more water
  → Capillary Rise

Formulas (2)

• Viscous Force Between Layers, Reynolds Number and Critical Velocity · Reynolds number and critical velocity
  $$R_e = \frac{\rho v d}{\eta}, \qquad v_c = \frac{R_e\,\eta}{\rho d}$$
• Terminal Velocity · Terminal velocity (Stokes)
  $$v_t = \frac{2r^2(\rho - \sigma)g}{9\eta}$$

Watch out for (2)

• Thinking a viscous liquid turns turbulent sooner
  → Viscous Force Between Layers, Reynolds Number and Critical Velocity
• Scaling terminal velocity with volume
  → Terminal Velocity

Formulas (3)

• Continuity: Narrow Pipe, Faster Flow · Continuity
  $$A_1 v_1 = A_2 v_2 = Q$$
• Bernoulli's Theorem · Bernoulli, horizontal pipe
  $$P_1 + \tfrac{1}{2}\rho v_1^2 = P_2 + \tfrac{1}{2}\rho v_2^2$$
• Torricelli: Jets and Draining Tanks · Torricelli
  $$v = \sqrt{2gh}, \qquad t_{\text{drain}} \propto \sqrt{h}$$

Watch out for (3)

• Scaling speed with radius, not area
  → Continuity: Narrow Pipe, Faster Flow
• Putting the high pressure at the narrow part
  → Bernoulli's Theorem
• Measuring depth from the bottom
  → Torricelli: Jets and Draining Tanks