A fine wire of diameter D is positioned across a passage to determine flow velocity from heat transfer characteristics. Current is passed through the wire to heat it, and the heat is dissipated to the flowing fluid by convection. The resistance of the wire is determined from electrical measurements, and the temperature is known from the resistance. a. For a fluid of arbitrary Prandtl number, develop an expression for its velocity in terms of the difference between the temperature of the wire and the free stream temperature of the fluid. b. What is the velocity of an airstream at 1 atm and 25 degree C, if a wire of 0.5-mm diameter achieves a temperature of 40 degree C while dissipating 35 W/m?

Aseries circuit consists of a resistor with r = 20 ? , a capacitor with c = 0.01 f, and a decaying battery with e = 300e? 5t. if the initial charge is 0, find the charge as a function of time t

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

A100-watt light bulb illuminates a solar cell. the electricity from the solar cell operates a water pump that delivers 1 watt of power. what is the efficiency of the system?