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Lecture1_Solution

Lecture1_Solution
Lecture1_Solution

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建工学院土木系Dept. of Civil Engineering

Autumn 2008

Solution to Lecture 1

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建工学院土木系Dept. of Civil Engineering

Autumn 2008

1.3

?If p is a pressure, V a velocity, and ρa fluid density, what are the dimensions (in the MLT system) of (a)p /ρ, (b)pV ρ, and (c)p /ρV 2?

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建工学院土木系

Dept. of Civil Engineering Autumn 2008

1.18?An important dimensionless parameter in certain types of fluid flow problems is the Froude number defined as , where V is a velocity, g the acceleration of gravity, and , ?a length. Determine the value of the Froude

number for V = 10 ft/s, g = 32.2 ft/s2, and ?= 2 ft. Recalculate the Froude number using SI units for V , g , and ?. Explain the

significance of the results of these calculations. 4/62

建工学院土木系Dept. of Civil Engineering Autumn 2008

1.35

?For a parallel plate arrangement of the type shown in Fig. 1.3 it is found that when the distance between plates is 2 mm, a shearing stress of 150 Pa develops at the upper plate when it is pulled at a velocity of 1 m/s. Determine the viscosity of the fluid between the plates. Express your answer in SI units.

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建工学院土木系Dept. of Civil Engineering Autumn 2008

1.36

As shown in Video V1.2, the “no-slip”condition means that a fluid “sticks”to a solid surface.This is true for both fixed and moving surfaces. Let two layers of fluid be dragged along by the motion of an upper plate as shown in Fig. P1.54. The bottom plate is stationary. The top fluid puts a shear stress on the upper plate, and the lower fluid puts a shear stress on the bottom plate. Determine the ratio of these two shear stresses.

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建工学院土木系Dept. of Civil Engineering Autumn 2008

1.39

? A 25-mm-diameter shaft is pulled through a cylindrical bearing as shown in Fig. P1.57. The lubricant that fills the 0.3-mm gap between the shaft and bearing is an oil having a kinematic viscosity of 8.0 ×10?4 m2/s and a specific gravity of 0.91. Determine the force P required to pull the shaft at a velocity of 3 m/s. Assume the velocity distribution in the gap is linear.

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建工学院土木系

Dept. of Civil Engineering Autumn 2008

1.41

? A layer of water flows down an inclined fixed surface with the velocity profile shown in Fig. P1.59. Determine the magnitude and direction of the shearing stress that the water exerts on the fixed surface for U = 2 m/s and h = 0.1 m.

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建工学院土木系Dept. of Civil Engineering Autumn 2008

1.55

?As shown in Video V1.5, surface tension forces can be strong enough to allow a double-edge steel razor blade to “float”on water, but a single-edge blade will sink. Assume that the surface tension forces act at an angle θrelative to the water surface as shown in Fig. P1.84. (a)The mass of the double-edge blade is 0.64 ×10?3 kg, and the total length of its sides is 206 mm. Determine the value of θrequired to maintain equilibrium between the blade weight and the resultant surface tension force. (b)The mass of the single-edge blade is 2.61 ×10?3 kg, and the total length of its sides is 154 mm. Explain why this blade sinks. Support your answer with the necessary calculations

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建工学院土木系

Dept. of Civil Engineering Autumn 2008

1.59

?An open, clean glass tube, having a diameter of 3 mm, is inserted vertically into a dish of mercury at 20 °C. How far will the column of mercury in the tube be depressed?

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建工学院土木系

Dept. of Civil Engineering Autumn 2008

1.61(See “Walking on water”, Section 1.9.) (a)The water strider bug shown in Fig. P1.94 is supported on the surface of a pond by surface tension acting along the interface between the water and the bug's legs. Determine the minimum length of this interface needed to support the bug. Assume the bug weighs 10?4 N and the surface tension force acts vertically upwards. (b)Repeat part (a) if surface tension were to support a

person weighing 750 N. .

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