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Whirlpools
Whirlpools may be approximated by a series of vortices of same signs advected into an uniform flow.
(a) Consider two vortices of equal strength K = +1 located at (-2,) and (+2, 0). Estimate how far away the effect of the vortices is perceived to be that of an unique vortex. What would be the strength of that vortex?
(b) Consider two vortices of equal strength K = +1 located at (-2,) and (+2, 0) in a horizontal uniform flow V = +0.03. What are the stream function and velocity potential of the resulting flow motion.
A vane, 10 cm long and 8 cm in diameter, was pressed into soft clay at the bottom of a bore hole. Torque was applied and gradually increased 45 N-m when failure took place. Subsequently the vane rotated rapidly so as to completely remould the soil..
You plan to use a tank of total volume V= 10 m3 to remove a contaminant at concentration Cin = 1 g/m3 from a waste stream with a flow rate of Q = 1 m3/h. The reaction is first order with a rate constant k1 = 0.5 h-1.
Beam Deflection Solution, Derive an expression for the deflection due to shear for a cantilever beam of constant rectangular cross section, under action of a point load, P at free end.
If the load of 4000 lb is lifted by the screw described in Problem 9 at the rate of 0.5 in/s, compute the required rotational speed of the screw and the power required to drive it.
The true azimuth of line AB is 193 degrees 20'. The angle measured counterclockwise between line AB and another line AC is 205 degrees 10'. The true azimuth of line AC is:
The frame ACD is supported by ball-and-socket joints at A and D. The blue cable passes smoothly through the ring at B. If you assume the frame is weightless and P = 75 lbs. what is the tension in the cable?
A centrifugal water pump has an impeller with r1 = 4", r2 = 12", f1 = 160°, f2 = 170°. The impeller is 2" wide at the inlet end and ¾" at the outlet. For a speed of 1800 rpm, neglecting losses and vane thickness
A fireman reduces the exit area on a nozzle so that the velocity inside the hose is quite small relative to the exiting velocity. What is the maximum exiting velocity and what is the maximum height the water can reach if the pressure inside the hose ..
The homogeneous gate shown in Fig. P2.88 consists of one quarter of a circular cylinder and is used to maintain a water depth of 4 m. That is, when the water depth exceeds 4 m, the gate opens slightly and lets the water flow under it. Determine the w..
Determine the downward acceleration α of the frame at which the contact at B will separate and break the electrical circuit.
A flow of 90 cfs is carried in a rectangular channel 10ft wide at a depth of 1.6 ft. If the channel is made of smooth concrete (n=0.016), find the slope necessary to sustain a uniform flow at this depth.
A drop of water forms under a solid surface. assume the drop has the shape of a hemisphere just before seperating. find an expression for the diameter, D, of the droplet, in terms of the specific weight and surface tension, assuming the contact angle..
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