Check my A vertical concentric annulus with outer radius ro and inner radius is lowered into a fluid of surface tension Y and contact angle 8< 90°. Derive an expression for the capillary rise h in the annular gap if the gap is very narrow.
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- (a) At a sudden contraction in a pipe the diameter changes from D, to D2. The pressure drop, Ap, which develops across the contraction, is a funetion of D and D2, as well as the velocity in the larger pipe section (V), and the fluid density (p), and viscosity (4). Use D1, V, and u as the repeating variables to determine a suitable set of dimensionless parameters. (b) A liquid flows with a velocity V through a hole in the side of a large tank. Assume that, V = f (h, g, p, o), where h is the depth of fluid above the hole, g is the www acceleration of gravity, p is the fluid density, and o is the surface tension. The data in the following table were obtained for measuring V by changing h, with a fluid having a density p= 10° kg/m' and surface tension o= 0.074 N/m. Perform a dimensional analysis to obtain a suitable set of dimensionless parameters, and calculate their corresponding values by using the dataset in the following table. V (m/s) h (m) 3.13 0.50 4.43 1.00 5.42 1.50 6.25 2.00…Given is a thin-walled tube with the following data: Determine the following: a. Enclosed Area Wall thickness- 2mm b. Perimeter of the thin walled tube ABC is a sector with a radius of 50 mm c. Shear flow AOD & COD is a triangle Torque is 1000 N.m Length of the thin walled tube is 0.5 m Use G=24 GPa for aluminium d. Shear stress e. Angle of twist A R 90° в D 3RFind the capillary rise (h) in the tube shown in the figure for a water-air-glass interface with 9= 20 if the tube %3D diameter (D) is 3 mm and the temperature is 20 C. Take surface tension (o) = 0.2 N/m. D
- is 0.25 m². Find: i) Фy and w, The power required to keep the plate in steady motion ii) PROBLEM 7 The velocity distribution in a pipe of radius ro is given by: m Annular when m<1 Ring Vm Find the momentum correction factor B +dr ro PROBLEM 8 Viscous (laminar) of oil takes place down the slope between parallel plates, 8mm apart, held inclined at 30° to the horizontal. The oil of viscosity 0.92 kg/ms and of mass density 1320 kg/m³. The pressure of two points, Im vertically apart, are 40KN/m² and 170 kN/m², when the upper plates moves at 0.3 m/s . velocity relative to the lower plate in the direction opposite to the oil flow. Determine: i) ii) iii) Maximum velocity of the flow within the oil medium The shear stress on the top plate The rate of oil flow per metre width 170 kN/m? 40 kN/m? U = 0.3 ms-1 Upper Plate 1m 8 mm (Datum) Direction of oil flow Lower Plate 30 PROBLEM 9 A siphon has rectangular throat section 2.2 m wide and the radius of the crown and crest ara 3m and 1.6m…A vertical triangular gate with Alcohol (SG = 0.78) on one side is shown in the %3D figure. Determine the total resultant force acting on the gate and the location of the center of pressure. 6 ft 3ft VAVAVAVAVA Ib f Unit weight of the liquid (y) Value of hbar (h) Arca of the rectangular gate (A) Hydrostatic Force (F) Vahe of (Igx) Vahue of ybar (9) Location of the Hydro. Force measured from the water surface of the gate inclined (yel Ib ft ***answer Hydrostatic Force Fon the box below: Answer: 1311.03 The correct answer is: 1022.1Which one is correct? A. Increasing additional load means increasing exposed depth in a fluid. B. Decreasing additional load means increasing submerged depth in a fluid. O A is false and B is false O A is false and B is true O A is true and B is false O Ais true and B is true
- 3. The tank shown has a parabolic curve gate at the bottom right side of length h perpendicular to the paper. The parabola has a vertex at the center of the hinge A. The parabola is defined by the equation in the X-Y coordinate system as shown. Neglecting the weight of the gate and the vertical reaction at the bottom end B of the gate, show the following if the unit weight of the liquid is y. (a) The magnitude of horizontal component of the hydrostatic force on the curve AB is 4.5yh³. 14 (b) The location of the horizontal component is ―h below 17 the x axis. (c)The magnitude of the vertical component of the hydrostatic force on the curve AB is yh³. 26 3 (e)The magnitude of the horizontal force P just to prevent the opening is yh³. Liquid surface 27 (d) The location of the vertical component ish from the y axis is 26 124 3 4h 27 - h. 26 hinge 2hDetermine the horizontal and vertical components of the liquid pressure acting on the semicylindrical gate ABC, as shown in the figure. The width into the paper is 1 m. 1m Liquid (s.g. = 0.88 ) 4 m B 2.6 m 1 m 幸 +A cylindrical thin-walled pressure vessel with radius r, wall thickness t, Poisson's ratio v, and modulus of elasticity E, is subjected to internal pressure p. Find the change in radius of the cylinder due to longitudinal loading only.
- The wall shear stress Tw for a flow in a narrow annular gap between a fixed and a rotating cylinder is a function of density p, viscosity , angular velocity 22, outer radius R and gap width Ar a) Show that (p, Q, R) can be used as repeating variables. b) Rewrite this relation in dimensionless form by using the exponent for T, and Ar as 1, and the exponent for μ as -1.STRESS IN THIN-WALLED CYLINDER Formulas: O = PD/2t + tangential Stress OL = PD/4t + longitudinal Stress Where: P = pressure inside the tank D= inside diameter of tank t= thickness of plate used for the cylinder PROBLEM 4: CE Brd Exam A 3m diameter x 6m high water tank is made up of 12mm thick steel plate. 4a. When full of water, find the circumfe-rential stress. а. 7.36 MPа c. 5.87 MPa b. 7.21 MPa d. 7.33 MPa 4b. When full of water, find the longitudinal stress. а. 4.29 MPa b. 4.05 MPa c. 2.66 MPa 4c. If plate stress is limited to 5 MPa, find the maximum height for said cylinder. a. 4.35 m c. 3.48 m d. 3.68 MPa b. 4.08 m d. 4.27 mAll of the following cause the Bernoulli effect excepta. Flow bottom roughnessb. Differences in grain size in bed loadc. Change of speed.d. Laminar current