Define dynamic viscosity and give the mathematical formula

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Reference no: EM133006756

Fluid Mechanics Static & Dynamic Fluid Systems

Learning Outcomes
Personal & Transferable Skills

1 Demonstrate numerical skills in the calculation of static and dynamic fluid systems.
Research, Knowledge & Cognitive Skills

2 Describe and explain the principles and application of hydraulic machines.

3 Analyse static and fluid flow systems.
Professional Skills

4 Apply the theory of viscosity in fluids to engineering situations.

Question 1 Compare liquids and gases with regard to their:
• shape
• volume occupied
• density
• viscosity
• compressibility

Question 2 (a) Define dynamic viscosity and give the mathematical formula for Newton's law of viscosity.
(b) How does kinematic viscosity differ from dynamic viscosity?
(c) Explain why viscosity is an important property in Fluid Mechanics.
(d) Name three classes of non-Newtonian fluids and explain how their viscosity is affected by factors other than temperature.
(e) What is the main difference between an ‘ideal' fluid and a ‘real' fluid?

Question 3 (a) Often the mathematics of a problem in Fluid Mechanics is made easier if we assume the mass or area to be concentrated at a single point. What are these points known as for:
(i) mass;
(ii) area.
(b) (i) Determine the centroid of the shape, as shown in Figure 1 (note that the circles are holes:

Figure 1

(ii) Determine the second moment of area of this shape and hence its radius of gyration about the axis a-a.

Question 4 (a) What is the formula for calculating the pressure due to the height of liquid?

(b) Name two devices which make use of this formula when used for pressure measurement.

(c) (i) In the situation shown in Figure 2, calculate the pressure difference between points 1 and 2 for the flow of a gas within the pipe. The liquid present is mercury whose density is 13560 kgm-3.

Figure 2

(ii) The liquid is now replaced by a new liquid whose density is 2200 kgm-3. If the pressure difference remains constant, what will be the new difference in level between each limb?

(iii) What is the advantage of changing the liquid?

Question 5 A storage tank has the cross-sectional shape shown in Figure 3 and is of 1.2 m breadth. Calculate the resultant force acting on the inclined surface AB and its point of action.

The density of the liquid is 950 kgm-3 and take g = 9.81 ms-2.

Figure 3

Question 6 (a) Describe the operation of a device which uses hydraulic pressure.

(b) Define:

(i) force ratio;

(ii) movement ratio.

(c) It is required to lift a skip whose load total is 18 kN. Two simple lifting jacks are available, both having an effort piston diameter of 12 mm and a load piston diameter of 80 mm. The load is to be distributed equally between the two. Calculate:

(i) the force ratio and movement ratio of each jack;

(ii) the pressure within the hydraulic fluid.

Question 7 The diagram shown below represents a process for which a pump and associated pipework require to be correctly sized.

The liquid is to be pumped from the underground storage vessel which is vented to atmosphere (assume 1 bar pressure) to a pressurized container supported some distance above ground level. The pump is sited at ground level and must be capable of delivering 0.01 m s3 -1 with a maximum velocity of 1.8 ms-1.

Data:

Liquid density, ρ = 960 kgm-3
Liquid viscosity, μ = 0.081 Pas

(a) Calculate the theoretical diameter of the pipe; the nominal pipe diameter chosen from the table and the actual average velocity in the nominal pipe.

(b) Calculate Reynolds number for the process and hence the head loss due to friction. State any assumptions made.

(c) Using the following table for minor head losses, calculate the minor head losses for the system using both the equivalent length method and the number of velocity heads method. Compare the head losses estimated by each method.

(d) Calculate the head required for the pump and its power requirement assuming a 70% efficiency.

(e) If the same pump was later used to pump water from the lower reservoir to the upper reservoir, what flow rate of liquid could be achieved? (N.B. This may require an iterative solution).

` State any assumptions made.

Data:

Water density, ρ = 1000 kgm-3
Water viscosity, μ = 0.001 Pas

Reference no: EM133006756

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