1. The hydraulic radius RH is the ratio of the area of the tube to its volume.
a) true
b) false
Explanation: The hydraulic radius RH is defined as the ratio of the area of the tube to the wetted perimeter. It is used to generally designate the velocity of flow in engineering hydraulics.
2. The hydraulic radius RH of circular tube is given by ________
a) RH=R/4
b) RH=R/6
c) RH=R/2
d) RH=R/12
Explanation: The hydraulic radius RH is defined as the ratio of the area of the tube to the wetted perimeter.
∴ RH=A/P=πR2/2πR
∴ RH=R/2.
3. The hydraulic radius RH is related with the voids ratio as ________
a) RH=Vs/eAs
b) RH=eVsAs
c) RH=e/AsVs
d) RH=eVs/As
Explanation: The hydraulic radius RH is given by,
RH=A/P=AL/PL
AL=eVs
PL= As
∴ RH=eVs/As.
4. The quantity of flow for circular tube with respect to the hydraulic radius is given by ________
a) \(q=\frac{1}{2}\frac{γ_w R_H^2}{η} \)
b) \(q=\frac{1}{2}\frac{γ_w R_H^2}{η}ia\)
c) \(q=\frac{1}{2}\frac{γ_w R_H^2}{η}i\)
d) \(q=\frac{1}{2}\frac{γ_w R_H^2}{η}a \)
Explanation: The quantity of flow for the capillary tube of any geometrical shape is given by,
\(q=C_S \frac{γ_w R_H^2}{η}ia\), where Cs is the shape constant.
For circular tube Cs=1/2
\( ∴ q=\frac{1}{2}\frac{γ_w R_H^2}{η}ia.\)
5. The relationship between the quantity of flow with respect to the hydraulic radius and the voids ratio is given by ________
a) \(q=\frac{γ_w R_H^2}{η}\frac{e}{1+e}iA\)
b) \(=C_S\frac{γ_w R_H^2}{η}\frac{e}{1+e}\)
c) \(=C_S\frac{γ_w R_H^2}{η}iA\)
d) \(=C_S\frac{γ_w R_H^2}{η}\frac{e}{1+e}iA\)
Explanation: Let the total cross-section of the soil be A and the porosity be n,
∴ a=nA
∴ \(q=\frac{1}{2}\frac{γ_w R_H^2}{η}ia=\frac{1}{2}\frac{γ_w R_H^2}{η}inA\)
Since n=e/(1+e),
∴ \(q=C_S \frac{γ_w R_H^2}{η}\frac{e}{1+e}iA.\)
6. Based on Allen Hazen experiments, permeability can be expressed as ___________
a) K=CD102
b) K=CD210
c) K=DC210
d) K=DC102
Explanation: In 1892, Allen Hazen based on his experiment on filter of sand particles between 0.1 and 3 mm, found that the permeability can be expressed as K=CD102.
7. Which of the following factors affects the permeability of soil?
a) Grain size
b) Properties of pore fluid
c) Void ratio of soils
d) All of the mentioned
Explanation: Grain size, properties of pore fluid, structural soil arrangement of soil particles, entrapped air and foreign matter and adsorbed water.
8. Physical permeability of a soil KP is related to the coefficient of permeability by the equation ___________
a) KP=kɳ
b) KP=kɳ/γW
c) KP=k/ɳ
d) KP=k γW
Explanation: In 1937, Muskat pointed out a relationship between physical permeability and Darcy’s coefficient of permeability as KP=kɳ/γW.
9. Loudon’s experiments demonstrated the relationship between _____________
a) Permeability and specific surface
b) Permeability and grain size
c) Permeability and adsorbed water
d) Permeability and volume
Explanation: Loudon’s experiment demonstrated that the permeability of coarse grained soils is inversely proportional to the specific surface at a given porosity.
10. What is the constant value of a and b in Loudon’s empirical formula “log10(KSs2) = a + bn”?
a) 1 and 0
b) 1.515 and 1.365
c) 1.365 and 1.515
d) 0 and 1
Explanation: Based on his experiments, Loudon found out the value of a and b s 1.365 and 1.515 for permeability of 10°c.