Mechanical Properties Of Fluid

Step 1: Concept
Flow becomes turbulent when the velocity exceeds a certain limit known as critical velocity.
Step 2: Analysis
In streamline flow, the velocity at the walls is zero. However, in turbulent flow, the behavior changes.
Step 3: Conclusion
For turbulent flow, the velocity of the liquid in contact with the walls is equal to the critical velocity.
Final Answer: (D)

Step 1: Concept
Surface energy .
Step 2: Analysis
Volume of big drop . Since , the radius of the big drop or . Change in energy . Substituting and : .
Step 3: Conclusion
The change in surface energy is .
Final Answer: (A)

Step 1: Concept
Wetting depends on the relative strength of cohesive and adhesive forces.
Step 2: Analysis
When cohesive forces are stronger than adhesive forces, the liquid forms droplets and does not spread.
Step 3: Conclusion
This condition results in a convex meniscus and an obtuse angle of contact.
Final Answer: (B)

Step 1: Concept
Pressure difference across a curved liquid surface is due to surface tension.
Step 2: Analysis
A soap bubble has two surfaces (inner and outer). Each contributes to the excess pressure.
Step 3: Conclusion
Total excess pressure .
Final Answer: (B)

Step 1: Concept
The stability of metal oxides generally increases with the electropositive character of the metal.
Step 2: Comparison
Magnesium is the most electropositive among the given metals, making the most stable oxide. Iron is the least electropositive, making the least stable.
Step 3: Conclusion
The correct increasing order of stability is: .
Final Answer: (c)

Step 1: Process
In a blast furnace, different zones have different temperature ranges for various chemical reactions.
Step 2: Slag Zone
The slag formation zone is where calcium oxide reacts with silica to form molten calcium silicate (slag).
Step 3: Temperature
The typical temperature maintained in this specific zone of the blast furnace is between .
Final Answer: (d)

Step 1: Calculate Molarity of Urea
6% solution means 6g in 100mL. Molecular weight of urea is 60.
Molarity M.
Step 2: Isotonic Condition
Solutions are isotonic if they have the same molar concentration (osmotic pressure).
Step 3: Conclusion
Since the urea solution is 1 M, it is isotonic with a 1 M solution of glucose.
Final Answer: (a)

Step 1: Determine Moles of
Number of moles of .
Step 2: Determine Equivalents
Number of equivalents of hydrogen .
Step 3: Apply Faraday's Law
Number of Faradays required . Current .
Step 4: Calculation
Current to be passed in one second A.
Final Answer: (b)

Step 1: Volume of a Soap Bubble.
The volume of a soap bubble is related to its radius by the formula: This volume is conserved when two soap bubbles coalesce under isothermal conditions.

Step 2: Total Volume Before Coalescence.
The total volume before coalescence is the sum of the volumes of both bubbles. If the radius of the first bubble is 3 cm and the radius of the second bubble is 4 cm, the total initial volume is:

Step 3: New Radius After Coalescence.
The volume of the new bubble is the same as the total initial volume: Equating the two volumes:

Step 1: Understand the Principle of Buoyancy.
The buoyant force acting on the cube is equal to the weight of the water displaced by the cube. The volume of the displaced water is equal to the submerged volume of the cube.

Step 2: Volume Submerged and Floating Condition.
The cube has a total volume of 10 cm , and 4 cm remains above the surface. Therefore, the submerged volume is:

Step 3: Use Archimedes’ Principle.
The buoyant force is equal to the weight of the displaced water. The weight of the displaced water is: Since the cube floats, the weight of the cube is equal to the buoyant force: Equating the two: Given that the density of water is , we get:

Step 1: Understanding the Concept:
Capillary rise . So .
Step 2: Detailed Explanation:
Given , .
.
Step 3: Final Answer:
Thus, height = .

Step 1: Understanding the Concept:
Bulk modulus .
Step 2: Detailed Explanation:
For an incompressible liquid, volume change is extremely small. In an idealized sense, it is sometimes taken as constant, leading to a very large but finite value. In simplified cases, it may be approximated as unity.
Step 3: Final Answer:
Thus, bulk modulus is taken as unity.

Concept: Floating condition:

Step 1: Apply buoyancy principle.
Half volume in oil and half in mercury:

Step 2: Simplify.


Step 3: Substitute values.
Thus, .

Concept: Capillary rise is given by:

Step 1: Given data

Step 2: Substitute values

Step 3: Solve for

Step 4: Diameter Final: