EFM HW 2 Due092617 liu ti li xue PDF

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sd01632100: Engineering Fluid Mechanics Homework#2 Due: Tuesday, September 26th, 2017 Instructions:  Homework is due at the beginning of the class on the date indicated above.  Solutions must be presented according to the “problem solving guideline” handed out during the first class (also available in syllabus). 1.

Solar ponds are small artificial lakes of a few meters deep that are used to store solar energy. The rise of heated (and thus less dense) water to the surface is prevented by adding salt at the pond bottom. In a typical salt gradient solar pond, the density of water increases in the gradient zone, as shown in the Figure, and the density can be expressed as

 πs    4H 

  0 1  tan2 

where ρ0 is the density on the water surface, is the vertical distance measured downward from the top of the gradient zone (s = −z) and H is the thickness of the gradient zone. For H = 4m, ρ0 = 1040kg/m3, and the thickness of 0.8m for the surface zone, (a) calculate the gage pressure at the bottom of the gradient zone, (b) plot variation of the pressure in the gradient zone as a function of depth. On the same graph, plot the hydrostatic pressure for the case of constant density at ρ0 = 1040kg/m3 for comparison (10 10 points points).

2.

Freshwater and seawater flowing in parallel horizontal pipelines are connected to each other by a double U-tube manometer, as shown. Determine the pressure difference between the two pipelines. Take the density of seawater at that location to be ρ = 1035kg/m3. Can the air column be ignored in this analysis (8 points) points)?

3.

The 500 kg load on the hydraulic lift shown in the Figure is to be raised by pouring oil (ρ = 1/4

780kg/m3) into a thin tube. Determine how high h should be in order to begin to raise the weight (5 5 points points).

4.

A closed tank is filled with water (60°F) and is fitted with a Bourdon gage that reads 7 psi. The tank is also fitted with a peizometer that is open to the atmosphere. Determine (9 9 points points): (a) the absolute pressure of the air in the top of the tank. (b) the gage pressure acting on the bottom of the tank. (c) the height of the column, h1.

5.

An inclined-tube manometer is constructed as shown. Derive a general expression for the liquid deflection, L, in the inclined tube, due to the applied pressure difference, Δp. Also, obtain an expression for the manometer sensitivity. Sensitivity of can defined as the ratio the deflection L in the inclined manometer to the deflection h in a simple U-tube manometer. Plot the sensitivity vs. d/ D and θ and discuss the effect of these two parameters on sensitivity. (15 points )

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6.

A 6m high, 5m wide rectangular plate blocks the end of a 5m deep freshwater channel, as shown in the Figure. The plate is hinged about a horizontal axis along its upper edge through a point A and is restrained from opening by a fixed ridge at point B. Determine the force exerted on the plate by the ridge. (15 points points)

7.

A concrete dam with a triangular cross-section is holding back water. The cross-section of the dam is shown in the schematic and has a depth of 15m. The concrete has a specific weight of 24 kN/m3 (20 20 points points). (a) Find the magnitude and location of the resultant force exerted on the dam by the water. (b) Find the moment of the resultant hydraulic force on the dam at point P. (c) To determine the reaction force that the foundation exerts on the dam base.

8.

Consider a heavy car submerged in water in a lake with a flat bottom. The driver’s side door of the car is 1.1m high and 0.9m wide, and the top edge of the door is 10m below the water surface. Determine the pressure force acting on the door if (a) the car is well-sealed and it contains air at atmospheric pressure and (b) the car is filled with water (15 15 points points).

9.

What causes buoyant force? Consider two identical spherical balls submerged in water at different depths. Will the buoyant forces acting on these two balls be the same or different? Explain (10 points).

10. The density of a liquid to be determined by an old 1-cm-diameter cylindrical hydrometer whose division marks are completely wiped out. The hydrometer is first dropped in water, and the water level is marked. The hydrometer is then dropped into the other liquid, and it is observed that the 3/4

mark for water has risen 0.6cm above the liquid-air interface. If the height of the original watermark is 13.6cm, determine the density of the liquid (15 15 points points).

11. Consider a large cubic ice block floating in seawater. The specific gravities of ice and seawater are 0.92 and 1.025, respectively. If a 15cm high portion of the ice block extends above the surface of the water, determine the height of the ice block below the surface (15 15 points points).

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