Second Semester Year 27 28 2y454

King Saud University College of Engineering Mechanical Engineering Department ME 381: FLUID MECHANICS time: 3 hours

Second Semester Final Examination (1427/1428 H)

Question 1 Is Reynolds number for laminar flow though a straight pipe is generally taken to be less than 300, 2300, or 4300? (b) For flow of water (µ = 0.001 kg/m-s: ρ = 1000 kg/m3) through a straight smooth pipe at 0.065 m3/hr, the pipe diameter for which transition to turbulence occurs is approximately equal to 1.0 cm, 1.5 cm, or 2.0 cm. (c) Water flows through an inclined 8-cm-diameter pipe. At section A and B the following data are taken: pA = 180 kPa, VA = 3.2 m/s, zA = 24.50 m, and pB = 260 kPa, VB = 3.2 m/s, zB = 9.21 m. Which way is the flow going? The pipe major loss is approximately equal to 7 m2/s2, 70 m2/s2, or 700 m2/s2. (a)

Question 2 (a) An idealized incompressible flow has the proposed three-dimensional velocity distribution

r r r r V = 4xy2 i + f (y) j - zy2 k

3 3 The appropriate form of the function f (y) equal to - y +c , - y + g(x) , 3 or - y +h(z) . (b) A two-dimensional steady incompressible flow has the u-component as 2 u = x y after discarding any constants of integration, the v-component is 2

2

2

3

given as v =- xy , v =- x y , or v =- xy . (c) A stream function of two-dimensional incompressible flow is given by y =k ( x2 - y2 ) where k is constant. The velocity field is given as

r r r r r r r r r V =- 2k ( yi + x j ) , V = 2k ( xi +y j ) , or V =- k ( yi + 2x j )

Question 3 (a) Water flowing in a smooth 6-cm-diameter pipe enters a venturi contraction with a throat diameter of 4 cm. Upstream pressure is 120 kPa and

the pressure in the throat is 50 kPa. Assuming frictionless flow, the flow rate is equal to 0.120 m3/s, 0.240 m3/s, or 0.50 m3/s. (b) A jet of water 3 cm in diameter strikes normal to a plate as shown. The force required holding the plate is 23 N. The jet velocity is equal to 10 m/s, 15 m/s, or 20 m/s.

The manometer shown reads 15 cm, SGHg = 13.6, and ρ water = 1000 kg/m . Assuming frictionless flow, the velocity of the water in the pipe is equal to 2 m/s, 4 m/s, 20m/s. (c)

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Question 4 (a) A droplet (sphere) of lubricating oil (SG=0.88) with diameter D=0.7

mm is placed in water. The resistance (drag force) to motion is FD= k V, where k =6.6x10-6 N. Volume of sphere is equal π D3/16. The magnitude of the terminal speed of the droplet is equal to 5 m/s, 10 m/s or 15 m/s.

(b) The can floats in the position What is its weight in Newton

shown. (N)?

(c) Water flows upward in a pipe slanted (inclined) at 30°. The mercury

manometer reads h = 12 cm. What is the pressure difference p1 – p2 in the pipe. Question 5 (a)

For the setup shown, the manometer reading H is 10 cm, 20 cm, or 30

cm.

A cube weighing 200 N and measuring 30 cm on a side is allowed to slide down an inclined surface at an angle 10° on which there is a film of oil having a viscosity of μ = 10-2 N-s/m2 and the oil has a thickness of 0.1 mm. The terminal velocity of the block is equal to 10 m/s, 20 m/s, or 30 m/s. (b)

(c)

State three basic laws that are used in the study of the fluid mechanics.

The right leg of the manometer is open to the atmosphere. Find the gage pressure, in Pa, in the air gap in the tank.

Gate AB is a homogeneous mass of 180 kg, 1.2 m wide into the paper, hinged at A, and resting on a smooth bottom at B. For what water depth h will the force at point B be zero? The density of glycerin, ρ = 1258 kg/m3.

The homogeneous 12-cm cube is balanced by a 2-kg mass on the beam scale when the cube is immersed in ethanol (ρ = 789 kg/m3). What is the specific gravity of the cube?

Water flows through the elbow and exits to the atmosphere. The pipe diameter is D1 = 10 cm, while D2 = 3 cm. The volume flow rate is 0.0150 m3/sec and the pressure p1 = 230 kPa (gage). Neglecting the weight of water and elbow, estimate the force on the flange bolts at section 1.

The 6-cm-diameter water jet strikes a plate containing a hole of 4-cm diameter. Part of the jet es through the hole, and part is deflected. Determine the horizontal force required to hold the plate.