In general decrease in temperature, results in
What is the radius of Mohr’s stress (in kPa) circle for a point inside a fluid mass which rotates like a solid body in a cylindrical container. The pressure at the point is 200 kPa.
Which one of the following is the bulk modulus K of a fluid? (Symbols have the usual meaning)
∴ dm = d(ρV)
0 = ρdV + Vdρ
−dV / V = dp / ρ
As per definition of Bulk Modulus
K = dp / (−dV / V)
K = dp / dρ/ρ
K = ρ dp / dρ
If angle of contact of a drop of liquid is acute, then
Which of the following fluids exhibit a certain shear stress at zero shear strain rate followed by a straight line relationship between shear stress and shear strain rate?
1 → Dilatants like quicksand, oobleck
2 → Newtonian fluids like water, air
3 → Pseudo plastics like blood, milk
4 → Bingham substances like mayonnaise, toothpaste
Bingham substances are those which undergo static deformation upto a limiting value (τ) of shear stress and behave as solids but beyond this limiting value they deform continuously and behave as fluids.
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An increase in pressure of a liquid from 7.5 MPa to 15 MPa results into 0.2 percent decrease in its volume. The coefficient of compressibility of the liquid in m2/N is
ΔV / V× 100 = −0.2
⇒ ΔV / V= −2 × 10-3
K = Δp / −Δ? / ?
= (15 − 7.5) × 106 / −(−2 × 10−3)
= 3.75 × 109
Compressibility = 1 / K = 2.666 × 10-10
≃ 0.267 × 10−9 m2/N
If the surface tension of water-air interface is 0.073 N/m, the gauge pressure inside a rain drop of 1 mm diameter will be
For the raindrop to be in equilibrium,
σπd = Δp × π / 4 d2
4σ d = Δp
Δp = 4 × 0.073 / 1 × 10-3
Δp = 292 N/m2
For the figure shown below, match List-I (curve) with List-II (type of fluid).
List-I (Curve) List-II (Type of fluid)
a. P 1. Newtonian fluid
b. Q 2. Pseudo plastic fluid
c. R 3. Dilatants
d. S 4. Bingham fluids
5. Ideal solid
6. Ideal fluids
Codes: a b c d
The vapour pressure is the characteristic fluid property involved in the phenomenon of
The absolute pressure inside a liquid jet is slightly greater than the atmospheric pressure. This excess pressure (p), the surface tension (σ) of the liquid and diameter (d) of jet are related as
⇒ p × (Ld) = σ × 2L
⇒ p = 2σ / d
The Mohr’s stress circle for any point considered inside a fluid at rest is given as
For a fluid at rest, shear stress at any plane passing through a point is zero hence all the planes are subjected to equal normal stress (pressure). Thus Mohr’s circle is a point on the −ve σ axis. And the distance of the point from origin is equal to pressure.
With increase in pressure, the bulk modulus of elasticity for an ideal gas
d(pVn) = 0
⇒ pnVn−1 dV + dp Vn = 0
⇒ dp = − 1 / npdV − np dV / V
⇒dp / (−dV / V) = np
⇒ K = np
Thus Bulk modulus of an ideal gas is directly dependent upon pressure i.e., if p ↑ K ↑
Assertion (A): An open glass tube is dipped in mercury. The mercury level inside the tube shall rise above the level of mercury outside.
Reason (R): The cohesive force between the molecules of mercury is greater than the adhesive force between mercury and glass.
Which of the following dimensionless no. represents applicability of concept of continuum analysis of a system?
Knudsen number is the ratio of the molecular mean free path length to a representative physical length scale.
The density of water is maximum at a temperature of
For any liquid the density of the liquid decreases with increasing temperature. But water is an exception and shows maximum density at 4.4°C.