Es2c5 exam paper january 19-20 PDF

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THE UNIVERSITY OF WARWICKSecond Year Examinations: January 2020DYNAMICS AND FLUID MECHANICSCandidates should answer ALL FOUR QUESTIONS (1-4).Time Allowed : 2 hours.Only calculators that conform to the list of models approved by the School of Engineering may be used in this examination. The Engineeri...

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ES2C50

THE UNIVERSITY OF WARWICK

Second Year Examinations: January 2020

DYNAMICS AND FLUID MECHANICS

Candidates should answer ALL FOUR QUESTIONS (1-4).

Time Allowed : 2 hours.

Only calculators that conform to the list of models approved by the School of Engineering may be used in this examination. The Engineering Databook and standard graph paper will be provided.

Read carefully the instructions on the answer book and make sure that the particulars required are entered on each answer book.

USE A SEPARATE ANSWER BOOK FOR SECTIONS A AND B

ES2C50 ______________________________________________________________________________ SECTION A : FLUID DYNAMICS ______________________________________________________________________________

1. (a) For axial flow through a circular tube, the Reynolds number for transition to turbulence is approximately 𝑅𝑒𝑐 = 2,300, based on the diameter, 𝑑 , and average velocity, 𝑈. If 𝑑 = 0.05 m and the fluid is kerosene with density 𝜌 = 804 kg m−3 and dynamic viscosity 𝜇 = 1.92 × 10−3 kg m−1 s−1 , find the volume flow rate in cubic metres per hour that causes transition.

(5 marks)

(b) The system in Fig. Q1b is open to atmosphere at point E, where the atmospheric pressure is 𝑝𝐸 = 101,325 Pa. If L  1.2 m what is the air pressure, p A , inside the container at point A? Neglect changes of the elevation pressure due to air in the system. (density mercury, (6 marks)  M  13,550 kg m 3 ; density water,  W  998 kg m 3 )

Fig. Q1b: Container connected through a partially liquid-filled tube to atmosphere.

Question 1 Continued Overleaf ... 1

ES2C50 Question 1 Continued (c) Fig. Q1c shows a cylindrical shaft rotating concentrically in a journal bearing. The clearance between the shaft and bearing is filled with oil of dynamic viscosity   0.1 N s m-2. The shaft rotates at a rate of 200 revolutions per minute, the shaft radius is R  50 mm, the clearance between the shaft and the bearing is h  0.1 mm and the length of the bearing (into the paper) is l  600 mm.

Fig. Q1c: Sketch illustrating the geometry of a rotating shaft inside a stationary bearing. (i) Draw a sketch illustrating the oil flow in the clearance between the shaft and the bearing. (2 marks) (ii) Find the viscous shear stress resisting the rotation of the shaft.

(3 marks)

(iii) Find the torque required to overcome the shear stress and to rotate the shaft .

(2 marks)

(iv) Find the power required to rotate the shaft.

(2 marks)

Question 1 Continued Overleaf …

2

ES2C50 Question 1 Continued (d) Figure Q1d shows two water tanks where water flows from one tank to the other one through a connecting pipe. The tanks are sufficiently large such that it can be assumed that the flow velocities in the tanks are negligible. Assuming no losses, estimate the volumetric flow rate by applying the Bernoulli equation between points (1) and (2). You will arrive at a contradiction. Briefly discuss what is wrong with this, seemingly innocent, problem. That is, what does the contradiction imply?

Fig. Q1d: Water flowing from one very large tank into another one. (5 marks)

(Total 25 marks)

_____________________________________________________________________________ Continued …

3

ES2C50 2. (a) An ideal fluid is ejected with a volumetric flow rate Q , from a small circular hole (diameter D ) in the wall of a large tank as illustrated in Fig. Q2a. Assume that Q depends only on the hole diameter, the fluid density and the pressure differencep  p 1  p 0 , where p1 and p0 are the pressure within the liquid at the height of the hole and the constant atmospheric pressure outside of the tank. Assume that the tank is large enough such that the fluid level inside the tank does not change appreciably during the time interval considered. Derive an expression for Q by dimensional analysis.

Fig. Q2a: Ideal fluid ejecting through hole from large tank. (6 marks) (b) Water flows through a circular nozzle, exits into the air as a jet, and strikes a flat plate, as shown in Figure Q2b. The force, 𝐹𝑃 , required to hold the plate was measured to be 70 N. Assuming steady, frictionless, one-dimensional flow estimate: (i) The velocities 𝑉1 and 𝑉2 at sections (1) and (2), where the nozzle diameters are respectively 𝐷1 and 𝐷2 as illustrated in Fig. Q2b. (7 marks) (ii) The mercury manometer reading h.

(7 marks)

(Note: Use for density water 𝜌𝑤 = 998 kg m−3 and for density mercury 𝜌𝑀 = 13,568 kg m−3 . Moreover, if your solution strategy requires knowledge of the atmospheric pressure then use 𝑝𝑎𝑡𝑚 = 101,325 Pa.)

Fig. Q2b: Water jet exiting from nozzle and striking a plate. Question 2 Continued Overleaf …

4

ES2C50

Question 2 Continued (c) The parabolic velocity profile for the two-dimensional, fully developed laminar flow between



flat parallel plates in Fig. Q2c. is given by u y   umax 1 



y2 h2

  where u max  0.6 mm s  1 is 

the maximum flow velocity, i.e. the velocity at y = 0, the mid level between the two plates. Find the volumetric flow rate for a section of length b = 20mm when h = 1.5mm.

Fig. Q2c: Fully developed laminar flow between parallel plates. (5 marks)

(Total 25 marks)

Continued …

5

ES2C50 ______________________________________________________________________________ SECTION B: DYNAMICS ______________________________________________________________________________ 3. a) A block of mass 1.2 kg slides down a frictionless slope with negligible air resistance. Initially (at t = 0) the block is travelling at a speed of 5 ms-1 down the slope, and is at a vertical distance of 3 m above ground level (y = 3 m), as illustrated in Fig. Q3a(i). Take the acceleration due to gravity as g = 9.81 m/s2. i)

Calculate the work done by gravity on the block between the block’s initial position (y = 3 m) and ground level (y = 0 m).

ii)

(2 marks)

Using energy methods, calculate the speed of the block at ground level

(3 marks)

b) The same block as in part (i) is released down the same slope with the same initial conditions, except now frictional forces act. If at t = 3 s the block is at ground level and the speed is equal to 7 ms-1, calculate the work done by friction on the block over the period 0 < t...