pressuretemperaturevelocitydensitystressspeed of soundspecific heatpressure gradient
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1.2 An equation linking water density and pressure is...where the pressure is in atmospheres and B.3000 atm. Determine the pressure in psi required to increase water density by 1% above its nominal value.
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1.3 Show that the unit vectors er and eθ in a cylindrical coordinate system are related to the unit vectors ex and ey by...and...
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1.4 Using the geometric relations given below and the chain rule for differentiation, show that...and...when r2=x2+y2 and tan θy/x.
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1.5 Find the pressure gradient at point (a,b) when the pressure field is given by...where ρ∞, v∞, a, and b are constants.
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1.6 Find the temperature gradient at point (a, b) at time t = (L2/α) ln e when the temperature field is given by...where T0, α, a, and b are constants.
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1.7 A scalar field is given by the function Φ = 3x2y + 4y2.
a. Find ...Φ at the point (3, 5).
b. Find the component of ...Φ that makes a 60° angle with the x axis at the point (3, 5).
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1.8 Given the following expression for the pressure field where x, y, and z are space coordinates, t is time, and P0, ρ, V∞, and L are constants. Find the pressure gradient...
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1.9 A vertical cylindrical tank having a base diameter of 10 m and a height of 5 m is filled to the top with water at 20°C. How much water will overflow if the water is heated to 80°C?
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1.10 A pressure of 10 MPa is applied to 0.25m3 of a liquid, causing a volume reduction of 0.005 cm3. Determine the bulk modulus of elasticity.
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1.11 Water in a container is originally at 100 kPa. The water is subjected to a pressure of 120 MPa. Determine the percentage decrease in its volume.
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1.12 Two clean and parallel glass plates, separated by a gap of 1.625 mm, are dipped in water. If σ=0.0735 N/m, determine how high the water will rise.
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1.13 Determine the capillary rise for a water-air-glass interface at 40°C in a clean glass tube having a radius of 1 mm.
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1.14 An open, clean glass tube, having a diameter of 3 mm, is inserted vertically into a dish of mercury at 20°C. Determine how far the column of mercury in the tube will be depressed for a contact angle of 130°.
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1.15 Determine the diameter of the glass tube necessary to keep the capillary-height change of water at 30°C less than 1 mm.
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1.16 A colleague is trying to measure the diameter of a capillary tube, something that is very difficult to physically accomplish. Since you are a Fluid Dynamics student, you know that the diameter can be easily calculated after doing a simple experiment. You take a clean glass capillary tube and place it in a container of pure water and observe that the water rises in the tube to a height of 17.5 millimeters. You take a sample of the water and measure the mass of 100 mls to be 97.18 grams and you measure the temperature of the water to be 80°C. Please calculate the diameter of your colleague’s capillary tube.
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