Engineering and Construction

fluid mechanics
LO3.1: determine head losses in pipeline flow
LO3.2: determine Reynolds’ number for a flow system and assess its significance
LO3.3: determine viscous drag of bluff and streamlined bodies
LO3.4: apply dimensional analysis to fluid flow
LO4.1: evaluate the impact of a jet of fluid on a moving vane
LO4.2: identify and explain the operating principles of water turbines and pumps
Task 1 – Learning Outcome 3.1
Determine head losses in pipeline flow

Q1: Calculate the flow of water under gravity in litres/sec between the two reservoirs in Figure 1 below.

5.6m

Pipe ø 11cm
in steel (k=0.20mm)

15.78m

Figure 1

Task 2 – Learning Outcome 3.2
Determine Reynolds’ number for a flow system and assess its significance

Q2:    As an engineer in an industry, you are required to pump oil (density 900 kg/m3, viscosity 0.12Ns/m2 and flow rate 0.2m3/s) in a 15 cm diameter pipe over a

distance of 120m.

(a)    Calculate the critical velocity and the Reynolds’ number in the pipe.

(b)    Calculate the power required (per metre) to pump the oil horizontally at a mass flow rate of 30kg/s.

(c)    Calculate the power required (per metre) to pump the oil horizontally at a mass flow rate of 120kg/s.

Task 3 – Learning Outcome 3.3
Determine viscous drag of bluff and streamlined bodies

Q3:
(a)    Describe the terms skin friction drag and form drag. (500 words excluding diagrams and tables; provide references for all your sources)

(b)    A car has an overall drag coefficient CD = 0.25 and a frontal area of A = 1.950m2. The density of air is  = 1.29kg/m3. The drag force is found from the

formula F = CD.1/2Av2 and the power from H = Fv. Calculate the power required from the car’s engine to overcome drag forces at a constant velocity of v = 30 m/s.

(c)    The thickness of a boundary layer δ on one side of a flat surface is given by the formula:

If the roof of the car can be approximated to a flat surface of length L = 2.60m and the viscosity of air is ɳ = 1.81×10-5Ns/m2, calculate the thickness of the boundary

layer at V = 30 m/s.

Task 4 – Learning Outcome 3.4
Apply dimensional analysis to fluid flow

Q4:
(a)    Show that the three terms of the Bernoulli equation      are dimensionally consistent.

(b)    Give the dimensional units of dynamic viscosity

(c)    Give the dimensional units of kinematic viscosity

(d)    Compare your dimensional units from Q2 and Q3 with the appropriate SI units of measure and comment on your findings.

Task 5 – Learning Outcome 4.1
Evaluate the impact of a jet of fluid on a moving vane

Q5:
(a)    A jet of water 25mm in diameter and having a velocity of 8.5 m/s strikes a flat plate. Calculate the force on the plate (a) if it is stationary, and (b) if it

moves in the same direction as the jet at 3.3 m/s

(b)    A jet of water issues from a nozzle under a pressure head of 45m and strikes normally against a fixed flat vane, exerting a force of 730N on the vane. What

must be the diameter of the nozzle?

(c)    The fixed vane is replaced with a series of flat vanes moving in the direction of the jet at a speed of 12 m/s, each normal to the jet. Calculate
(i)    the force exerted on the vanes,
(ii)    the input and output power to the machine and
(iii)    the efficiency of the system.

Task 6 – Learning Outcome 4.2
Identify and explain the operating principles of water turbines and pumps

Q6: For two types of pump or turbine, produce a summary of the operating principles and characteristics of each (1000 words excluding diagrams and tables; provide

references for all your sources)

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