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GATE’22 CE:- Daily Practice Quiz 09-Aug-2021

Quiz: Civil Engineering
Exam: GATE
Topic: Miscellaneous

Each question carries 2 marks
Negative marking: 1/3 mark
Time: 12 Minutes

Q1. The pH value of the incoming water is 7.2 and outgoing water is 8.4, assuming a linear variation of pH with time determine average pH value of water:
(a) 7.800
(b) 7.474
(c) 7.2
(d) 8.4

Q2. Crude oil of kinematic viscosity 2.25 stokes flows through a 20 cm diameter pipe, the rate of flow being 1.5 litres/s. the flow will be-
(a) Uncertain
(b) Laminar
(c) Turbulent
(d) Transition

Q3. The kinematic indeterminacy of the plane truss shown in the figure is

GATE'22 CE:- Daily Practice Quiz 09-Aug-2021 |_30.1
(a) 11
(b) 8
(c) 3
(d) 0

Q4. An RC structural member rectangular in cross section of width b and depth D is subjected to a combined action of bending moment M and torsional moment T. The longitudinal reinforcement shall be designed for a moment M_e given by
(a) M_e=M+T(1+D\/b)/1.7
(b) M_e=M+T(1-D\/b)/1.7
(c) M_e=T(1+D\/b)/1.7
(d) M_e=T(1-b\/D)/1.7

Q5. A watershed having an area of 4 km² is subjected to a rainfall event of 9 cm, thereby generating stream flow at the outlet of the watershed for 10 h. If the average stream flow rate at the outlet of the catchment is 5m³/s, occurring for a period of 10 h, the runoff co-efficient of the watershed for the storm is:
(a) 0.4
(b) 0.3
(c) 0.6
(d) 0.5

Solutions

S1. Ans.(b)
Sol. pH of incoming water = 7.2
pH of outgoing water = 8.4
Average pH value of water =?
pH = – log [H+]
7.2 = – log [H+]
Tanking anti log-
[H+] = 10^(-7.2)———— (1)
pH = – log [H+]
8.4 = – log [H+]
Tanking anti log-
[H+] = 10^(-8.4)———— (2)
Average concentration of [H+] = (10^(-7.2)+10^(-8.4))/2

Average pH = – log (10^(-7.2)+10^(-8.4))/2
= – log [3.35384×10^(-8) ]
= -(-7.47445762)
= 7.474

S2. Ans.(b)
Sol. Reynold’s no. = ρVd/μ=Vd/υ
V=Q/A=(1.5×10^(-3))/(π/4 〖(0.20)〗^2 )
V=(4×1.5×10^(-3))/(0.04×π)
V=0.0477 m\/sec
Re =Vd/υ=(0.0477×0.20)/(2.25×10^(-4) )=42.48
It is below than 2000 so the flow is laminar.

S3. Ans.(a)
Sol. No.of joints (j) =7
No.of external reactions (r_e) =3
Kinematic indeterminacy (D_k) =2j-r_e
=(2×7)-3
▭(D_k=11)

S4. Ans.(a)
Sol. Longitudinal reinforcement shall be designed to resist equivalent moment.
▭(Me= M+M_t )
▭(M_t=T/1.7 (1+D/b) )
▭(Me=M+T ((1+D\/b)/1.7) )
Equivalent shear
▭(Ve=V+ 1.6 T/b)

S5. Ans.(d)
Sol. Stream flow rate (Q) = 5m³/s
Duration (t) = 10 hour
Area (A) = 4km²
Rainfall (R)= 9cm
Run off volume = Q × t = 5 m³/s × 10 hour = 5 m³/s × 10 × 60 × 60 sec.
Total precipitation = A × R = 4 × (1000)^2× 0.09
Run off co-efficient =(Runoff volume)/(Total precipition)
=(5×10×60×60)/(4×(1000)^2×0.09)
=0.5

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