Fluid Mechanics - Study Mode

[#421] Stoke's law is valid, when N Re,p is less than
Correct Answer

(A) 2

[#422] Correction for capillary effect in manometers (used for pressure measurement) need not be applied, if diameter of the manometer tube is __________ mm.
Correct Answer

(C) > 12.5

[#423] Velocity of liquid hydrocarbon fuels in a pipeline can not be measured by magnetic flowmeters, because their __________ is very low/small.
Correct Answer

(B) Electrical conductivity

Explanation

Solution: Magnetic flowmeters work on the principle of electromagnetic induction . This means they rely on the liquid being measured to have some electrical conductivity . Here's a simplified explanation: Imagine the liquid flowing through a pipe surrounded by a magnetic field. If the liquid is electrically conductive , its moving through this field generates a small voltage. The flowmeter measures this voltage and relates it to the flow rate. Liquid hydrocarbon fuels (like gasoline or kerosene) are typically poor conductors of electricity. In other words, their electrical conductivity is very low. Therefore, if you try to use a magnetic flowmeter on a liquid hydrocarbon fuel, the signal generated will be too weak or nonexistent, making an accurate measurement impossible. Let's look at why the other options are less likely to be correct: Option A: Thermal conductivity: How well a substance conducts heat, while important in some applications, doesn't directly impact the operation of a magnetic flowmeter. Option C: Specific gravity: This is the ratio of the density of a substance to the density of water. While it relates to the fluid properties, it's not the primary factor affecting measurement in this type of flowmeter. Option D: Electrical resistivity: This is the opposite of electrical conductivity (how much a substance resists electrical current). While related, the more direct factor influencing the flowmeter's operation is the conductivity itself - whether it's high enough to generate a measurable signal.

[#424] For turbulent fluid flow in pipe, the expression for Prandtl one seventh power law is (where, r = pipe radius, x = distance).
Correct Answer

(A) $$frac{{ ext{V}}}{{{{ ext{V}}_{max }}}} = {left( {frac{{ ext{x}}}{{ ext{r}}}} ight)^{frac{1}{7}}}$$

[#425] Capillary rise of mercury in a small diameter tube is proportional to (where, d = diameter of the tube, σ = surface tension of mercury)
Correct Answer

(C) $$sigma $$

Explanation

Solution: The capillary rise of mercury in a small diameter tube is proportional to 1/d , where d is the diameter of the tube, and σ is the surface tension of mercury. Capillary rise occurs due to the balance between cohesive forces within the liquid and adhesive forces between the liquid and the tube wall. In a small diameter tube, the capillary rise is inversely proportional to the diameter of the tube. Mathematically, the capillary rise h is given by the capillary rise equation: h = (2σ cosθ) / (ρgr) Where: σ is the surface tension of the liquid (mercury). θ is the contact angle between the liquid and the tube wall (usually close to 0° for mercury in glass). ρ is the density of the liquid (mercury). g is the acceleration due to gravity. r is the radius of the tube (half of the diameter). Since the radius r is directly proportional to 1/d , and the capillary rise is proportional to the radius r , the capillary rise is inversely proportional to the diameter d , which is represented by option B.