Concept explainers
Consider the milk container of Example 1.4.2 (Figure 1.4.7). A straw 9.5 cm long was inserted in the side of the container. While adjusting the tap flow to keep the water height Constant, the time for the outflow to fill a 250-ml cup was measured. This was repeated for several heights. The data are given in the following table.
Obtain a functional description of the volume outflow rate f through the straw as a function of water height h above the hole.
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System Dynamics
- The data listed below is from a passenger hot air balloon. The balloon is designed to lift 10-people (80 kg each person). The balloon consists of a basket, a burner- propane tank system. It will lift up when the cold air trapped inside warms up by the burner. Density of air inside the balloon is 99°C: 0.9486 kg/m³, density of air outside balloon is 20°C (ambient): 1.2041 kg/m³ Mass (kg) Balloon Basket Burner Propane tank 113.4 kg 63.5 kg 22.7 kg 183.7 kg Assume the balloon is a sphere shape, volume =(4/3)pi R3. a. Determine the minimum diameter of the balloon that would have a total lifting force to balance the weight of balloon, basket, burner, propane tank and 10 people? b. If the balloon is converted to survey the weather, it will be filled with hydrogen gas (H2). Assume the weight of the people (800kg) is now replaced by onboard equipment, what is minimum diameter needed to keep it afloat at 18km above the surface of the earth?arrow_forwardA physics lab consists of a large ball attached to a wire. Students hold on to one end of the wire, then whirl the ball around in circles and count the number of rotations per second. One group finds these numbers: ball mass= 320 gram, wire length= 1.3m, number of rotations/sec=2.5. The wire is made of steel with a diameter of 1mm and a Young's modulus of 20x10^10 N/m^2.How much does the wire stretch due to the tension on it? Should the students correct their data for the wire stretching?arrow_forwardThe speed of sound traveling through the sea is a function of temperature, salinity, and pressure. It is modeled by the function C = 1449.2 + 4.67T -0.055T² +0.00029T³ + (1.34-0.01T) (S-35) + 0.016D where C is the speed of sound (in meters per second), T is the temperature (in degrees Celsius), S is the salinity (the concentration of salts in parts per thousand, which means grams of dissolved solids per 1000 grams of water), and D is the depth below the sea surface, in meters. Calculate the following (Check attached image d3) when T = 10 °C, S = 35 parts per thousand, and D = 100 m. Explain the physical meaning of these derivatives.arrow_forward
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