1. KINEMATICS
1. A nozzle is so shaped that the velocity of flow along the centre line changes linearly from 1.5 m/s to 15 m/s in a distance of m. Determine the magnitude of the convective acceleration at the beginning and end of this distance. Answer: 54 m/s2 and 540 m/s2 2. If for two-Dimensional flow the stream function is given by ¥=2xy, calculate the velocity at the point (3,6). Show that the velocity potential ø exists for this case and deduce it. Also draw the streamlines corresponding to ¥=100 and ¥=300 and equipotential lines correspond to ø=100 and ø=300. Answer: m/s

2. Fluid Mechanics
3.The velocity components of two- Dimensional plane motion of a fluid are
u= 𝑦 2 − 𝑥 2 (𝑥 2 + 𝑦 2 )2 and v= - 2𝑥𝑦 (𝑥 2 + 𝑦 2 )2
Show that the fluid is compressible and flow is irrotational.
Show that the points (2,2) and (1,2-√3) are located on the same streamline.
Determine the discharge across a line joining point (1,1) and (2,2) given that the thickness of the fluid stream normal to the x-y plane is t.
Answer: t/4 𝑚 3 /s
4.The velocity components in a two dimensional flow field for an incompressible fluid are expressed as u= 𝑦 x −x 𝑦 2 ; v=x 𝑦 2 −2𝑦− 𝑥 3 3
Show that these functions represent a possible case of an irrotational flow.
Obtain an expression for stream function ¥.
Obtain an expression for velocity potential ø.

3. 5. For a three dimensional flow field described by
Fluid Mechanics
5. For a three dimensional flow field described by
v= ( 𝑦 2 + 𝑧 2 )𝑖+ 𝑥 2 + 𝑧 2 𝑗+ 𝑥 2 + 𝑦 2 𝑘
Find at (1,2,3)
The components of acceleration
The components of rotation
Answer: (70,56,66) ;(-1,2,-1)

4. Fluid Mechanics
6. The water level in a tank is 2 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank cover is airtight, and the air pressure above the water surface is 2 atm gage. The system is at sea level. Determine the maximum height to which the water stream could rise.
Answer: 40.7 m

5. Fluid Mechanics
7. Air flows through a pipe at a rate 170 L/s. The pipe consists of two sections of diameter 18 cm and 10 cm with a smooth reducing section that connected them. The pressure difference between the two pipe sections is measured by a water manometer .Neglecting frictional effects, determine the differential height of water between the two pipe sections. Take the air density to be 1.20 kg/ 𝑚 3 .
Air
170 L/s
18 cm
10 cm
Answer: 2.60 cm

6. Fluid Mechanics
8. A 2 m high large tank is initially filled with water. The tank water surface is open to the atmosphere, and a sharp-edged 1 cm diameter orifice at the bottom drains to the atmosphere through a horizontal 1m long pipe. If the total irreversible head loss of the system is determined to be 1 m, determine the initial velocity of the water from the tank. Disregard the effect of the kinetic energy correction factors. Answer: m/s
Answer: 3.13 m/s

7. Fluid Mechanics
9.Water is pumped from a lake to a storage tank 18 m above at a rate of 70 L/s while consuming 20.4 kW of electric power. Disregarding any frictional losses in the pipes and any changes in kinetic energy, determine (a) the overall efficiency of the pump– motor unit and (b ) the pressure difference between the inlet and the exit of the pump.
18 m

8. Fluid Mechanics
10. In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by v= 𝑢 𝑜 1+ 3𝑥 𝐿 𝑖,where x is the distance along the axis of the nozzle from its inlet plane and L is the length of the nozzle. The time required for a fluid particle on the axis to travel from the inlet to the exit plane of the nozzle is Answer: 𝐿 3 𝑢 𝑜 𝑙𝑛4