SSC JE Fluid Mechanics Questions with Detailed Solutions

Specific gravity : Specific gravity is defined as the ratio of density of fluid to the density of standard fluid.
• In liquid standard fluid is taken as water.
• In gas standard fluid is taken as air.
Specific gravity of different fluid :
i) Mercury : 13.6
ii) Water : 1
iii) Oil : 0.7 to 0.9

Surface tension : Surface tension is a phenomenon due to which the exposed liquid behaves like a stretched membrane
• When a liquid is exposed to the air it behaves like a stretched membrane as the water molecule are attracted to each other.
Surface tension (σ)

Unit of surface tension = N/m
• Capillary action is an effect of surface tension that is only applicable to small tube that contain liquids.

The major loss of energy or head is due to friction.
Minor losses:
Minor energy (head) loss occurs in the following cases-
1. Loss of head due to sudden enlargement.
2. Loss of head due to sudden contraction.
3. Loss of head due to an obstruction in the pipe.
4. Loss of head at the entrance to a pipe.
5. Loss of head at the exit to a pipe.
6. Loss of head due to bend in the pipe, and
7. Loss of head in various pipe fittings.

Pipes in series combination:
-Pipes are said to be in series if they are connected end-to-end (in continuity with each other) so that the fluid flows in a continuous line without branching.
-Discharge in each pipe is constant.
-Head loss in each pipe is different.
Pipes in parallel combination:
-The main pipeline divides into two or more parallel pipes and then reunites (or join) into a single pipe downstream.
-The head loss in each pipe is the same.

Conditions for the most economical or efficient section:
From Chezys and Mannings equation that the velocity of flow will be maximum when hydraulic radius R will be maximum for factors like the slope of bed, and surface roughness being constant.
Hydraulic radius is maximum if the wetted perimeter is minimum.
Most economical rectangular section:
Width of the channel is twice the depth of flow (B = 2y).
Hydraulic radius is half of the depth of flow. (R= y/2)
Most economical trapezoidal section:
Half of the top width must be equal to the sloping side.
The hydraulic radius must be half the depth of water.
Most economical triangular section:
The side slope has to be inclined at 45∘.
Hydraulic radius (R) =

​ Most economical circular section:
The depth of flow(y) = 0.81D. (for maximum velocity)
The hydraulic radius(R) for maximum velocity is 0.3 D
The depth of flow(y) = 0.95D. (for maximum discharge)
Where D = Diameter of channel

Pipes in series combination:
 Pipes are said to be in series if they are connected end-to-end (in continuity with each other) so that the fluid flows in a continuous line without branching.
 Discharge in each pipe is constant.
 Head loss in each pipe is different.
Pipes in parallel combination:
 The main pipeline divides into two or more parallel pipes and then reunites (or join) into a single pipe downstream.
 The head loss in each pipe is the same.

Given, Diameter of pipe = 0.5 m, Discharge = 0.8 m³/sec , Friction factor = 0.03 
water required to be lift by pump from R.L 92.00 m to R.L 108.00 m => Static head required to calculate capacity of pump (H) = difference between R.L at delivery and source point 
∴ static head required = 108.00 - 92.00 = 16.00 m

Types of flow :
i) Steady flow : The flow in which flow condition like velocity, pressure does not changes with time is known as steady flow.
ii) Unsteady flow : The flow in which flow condition like velocity,pressure can changes with time is known as unsteady flow.
iii) Uniform flow : The type of flow in which the velocity at any given time does not changes with respect to space.
iv) Non-uniform flow : The type of flow in which the velocity at any given time changes with respect to space.
v) Laminar flow : The type of flow in which fluid particle move along well defined path or stream line and all stream lines are straight and parallel.