A large container is filled with liquid of density 1.1 x10 3 kg/m 3 A small hole

Question

A large container is filled with liquid of density 1.1 x103 kg/m3 A small hole of area 2.5 x 10-6 is opened in side of container a distance h belowliquid surface. A stream of liquid flows through hole intobeaker placed to right of container. At same time liquid isadded to container at appropriate rate so that h remainsconsant. Amount of liquid collected in beaker in 2.0 minutesis 7.2 x 10 -4 m3 Calculate volume rate of flow of liquid from hole Calculate speed of liquid as it exits from hole Calculate height, h, of liquid needed above hole to causespeed found above The height of hole from table is .5 m How far from sideof container does liquid hit table? Suppose there is now lessliquid in container so that height h is reduced to h/2  This is height above hole. If a beaker was placed on tabletopand water entered beaker from container when height was h, thenwhere will liquid hit tabletop now?   to left of beaker ,same spot, to right of beaker A large container is filled with liquid of density 1.1 x103 kg/m3 A small hole of area 2.5 x 10-6 is opened in side of container a distance h belowliquid surface. A stream of liquid flows through hole intobeaker placed to right of container. At same time liquid isadded to container at appropriate rate so that h remainsconsant. Amount of liquid collected in beaker in 2.0 minutesis 7.2 x 10 -4 m3 Calculate volume rate of flow of liquid from hole Calculate speed of liquid as it exits from hole Calculate height, h, of liquid needed above hole to causespeed found above The height of hole from table is .5 m How far from sideof container does liquid hit table? Suppose there is now lessliquid in container so that height h is reduced to h/2  This is height above hole. If a beaker was placed on tabletopand water entered beaker from container when height was h, thenwhere will liquid hit tabletop now?   to left of beaker ,same spot, to right of beaker Calculate volume rate of flow of liquid from hole Calculate speed of liquid as it exits from hole Calculate height, h, of liquid needed above hole to causespeed found above The height of hole from table is .5 m How far from sideof container does liquid hit table? Suppose there is now lessliquid in container so that height h is reduced to h/2  This is height above hole. If a beaker was placed on tabletopand water entered beaker from container when height was h, thenwhere will liquid hit tabletop now?   to left of beaker ,same spot, to right of beaker

Explanation / Answer

(a) flow rate = volume / time = 0.00072 / 120 seconds =    6.00 x10-6 m3/s . (b)   speed =   flow rate /area = 6.00 x 10-6 / 2.5 x10-6= 2.4 m/s . (c)   h = v2 / 2g = 2.42 / 2*9.80 =    0.294meter . (d) This is projectile motion...   vertical motiongives the time for the water to hit the table: .         t = 2H/g = 2*0.5/9.80 =   0.3194seconds .     water hits table atdistance    d = vt = 2.4 * 0.3194 =    0.767meters from the container. . (e) if the height in the container is reduced to h/2, thespeed of the fluid out the hole is reduced, so the distance is alsoreduced. It will now hit thetable between the container and the beaker. Whether this isto the right or left of the beaker just depends on which side ofthe table you're standing on... from one side, it would look liketo the left of the beaker; from the other side it would look liketo the right. If you had a picture to go with this, you couldanswer "left" or "right". Whichever it is, the water lands betweenthe container and the beaker.

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