Calculating a Velocity Using the Equation of Continuity

  • 1.

    Water is flowing in a tapered pipe. The area at the inlet of the pipe is {eq}2\ \rm cm^{2} {/eq} and the velocity of the water at the inlet of the pipe {eq}10\ \rm cm/s {/eq}. If the area at the outlet of the pipe is {eq}4\ \rm cm^{2} {/eq}, calculate the velocity of water at the outlet of the pipe.

    Answers:

    • 20 {eq}\rm cm/s {/eq}

    • 10 {eq}\rm cm/s {/eq}

    • 5 {eq}\rm cm/s {/eq}

    • 15 {eq}\rm cm/s {/eq}

  • 2.

    The velocity of the water flowing in pipe is {eq}30\ \rm m/s. {/eq} If the area of the pipe is reduced by 3 times, calculate the new velocity of the water.

    Answers:

    • 10 m/s

    • 90 m/s

    • 30 m/s

    • 60 m/s

  • 3.

    Blood is flowing in veins. Due to a contraction in the vein, the area of the vein reduces to 0.6 times the original area. If the velocity of the blood flowing in the vein is 12 m/s, calculate the velocity of blood at the contraction.

    Answers:

    • 7.2 m/s

    • 14.4 m/s

    • 20 m/s

    • 10 m/s

  • 4.

    In a pipeline, the area of the pipe reduces to 10 {eq}\rm cm^{2} {/eq} from {eq}20\ \rm cm^{2} {/eq}. If the velocity of water at {eq}20\ \rm cm^{2} {/eq} area is 50 cm/s, calculate the velocity of water in the pipeline where the area is {eq}10\ \rm cm^{2} {/eq}.

    Answers:

    • 100 cm/s

    • 25 cm/s

    • 50 cm/s

    • 75 cm/s

  • 5.

    Water is flowing in a pipe at a speed of 50 m/s. If the diameter of a pipe is reduced by 0.5 times, calculate the speed of the water at the reduction.

    Answers:

    • 100 m/s

    • 25m/s

    • 12.5 m/s

    • 200 m/s

  • 6.

    The velocity of water at the inlet of a {eq}3.5\ \rm cm {/eq} pipe is 35 cm/s. If the diameter of the pipe at the exit is 5 cm, calculate the velocity of the water at the exit of the pipe.

    Answers:

    • 18.15 cm/s

    • 17.15 cm/s

    • 19.15 cm/s

    • 16.15 cm/s

  • 7.

    If the area of the pipe decreases, the velocity of the water flowing in the pipe will

    Answers:

    • First increase then decrease

    • Does not change

    • Increase

    • Decrease

  • 8.

    A liquid enters a pipe of diameter {eq}d {/eq} with a velocity {eq}v {/eq}. If the diameter of the pipe is increased to {eq}2d {/eq} at the outlet, calculate the velocity of the water at the oultet of the pipe.

    Answers:

    • {eq}0.5v {/eq}

    • {eq}2v {/eq}

    • {eq}4v {/eq}

    • {eq}0.25v {/eq}

  • 9.

    If the diameter of a pipe converges to 0.4 times the initial diameter, the ratio of the velocity at the coverage to the velocity at the initial diameter is:

    Answers:

    • 6.25

    • 0.16

    • 0.25

    • 0.40

  • 10.

    The inlet diameter of a nozzle is {eq}8\ \rm cm {/eq} and the velocity of air entering the nozzle is {eq}20\ \rm cm/s {/eq}. Calculate the velocity of the air at the exit of the nozzle if the diameter at the exit is 4 cm.

    Answers:

    • 160 cm/s

    • 120 cm/s

    • 80 cm/s

    • 40 cm/s

  • 11.

    In a prototype testing of water turbine, the velocity at the exit of the nozzle having area {eq}2\ \rm cm^{2} {/eq} is {eq}10\ \rm cm/s {/eq}. Calculate the velocity at the inlet of the nozzle if the area at the inlet is {eq}3\ \rm cm^{2}. {/eq}

    Answers:

    • 15.0 cm/s

    • 6.67 cm/s

    • 13.3cm/s

    • 0.149 cm/s

  • 12.

    The blood velocity at the point of contraction is 10 cm/s. If the starting diameter of the vein is 1 cm and the diameter at the contraction is {eq}0.5\ \rm cm {/eq}, calculate the starting velocity of the blood.

    Answers:

    • 2.6 cm/s

    • 1.00 cm/s

    • 2.5 cm/s

    • 2.1 cm/s

  • 13.

    The blood velocity at the initial point is 25 cm/s. If the initial diameter of the vein is 0.2 cm and the diameter at the contraction (reduced section) is {eq}0.12\ \rm cm {/eq}, the velocity of the blood at contraction is?

    Answers:

    • 60.3 cm/s

    • 44.5 cm/s

    • 69.4 cm/s

    • 75.3 cm/s

  • 14.

    The velocity of the air at the inlet of pipe having diameter {eq}d_{1} {/eq} is {eq}v_{1} {/eq}. The diameter at the exit of the pipe is {eq}d_{2} {/eq}. The outlet velocity {eq}\rm v_{2} {/eq} of a fluid flowing in a pipe is represented by which of the following equation:

    Answers:

    • {eq}\rm \dfrac{d_{2}^{2}v_{1}}{d_{1}^{2}} {/eq}

    • {eq}\rm \dfrac{v_{1}^{2}d_{1}}{d_{2}} {/eq}

    • {eq}\rm \dfrac{d_{1}^{2}v_{1}}{d_{2}^{2}} {/eq}

    • {eq}\rm \dfrac{d_{1}v_{1}}{d_{2}} {/eq}

  • 15.

    A diffuser is used to slow down the air that passes through it. If the ratio of the diffuser's inlet to outlet area is 0.5, calculate the velocity ratio between the diffuser's inlet and outflow.

    Answers:

    • 1.0

    • 4.0

    • 2.0

    • 1.33

  • 16.

    The liquid entering the hose of diameter 1-inch has a velocity of 30 m/s. If the outlet diameter of the hose is 2-inch, calculate the velocity of the liquid leaving the hose.

    Answers:

    • 7.5 m/s

    • 1.875 m/s

    • 18.75 m/s

    • 15 m/s

  • 17.

    A sprinkler has 20 holes. The area of each hole is {eq}2 \ \rm cm^{2} {/eq}. The sprinkler is connected to a pipe of {eq}20\ \rm cm^{2} {/eq} area and the velocity of water in the pipe is 50 cm/s. Calculate the velocity of the water leaving the hole of the sprinkler.

    Answers:

    • 50 cm/s

    • 500 cm/s

    • 25 cm/s

    • 250 cm/s

  • 18.

    A liquid flows at a speed of 5 cm/s through a conduit with a diameter of 20 cm . What is the new velocity of the liquid if the pipe diameter is reduced to 8 cm?

    Answers:

    • 31.25 cm/s

    • 41.25 cm/s

    • 27.25 cm/s

    • 12.50 cm/s

  • 19.

    Air is flowing in a pipe. The area at the inlet of the pipe is {eq}8\ \rm in^{2} {/eq}. If the area at the exit of the pipe is {eq}12\ \rm in^{2} {/eq} and the velocity of the air is {eq}16\ \rm m/s {/eq}, calculate the velocity of the air at the inlet of the pipe.

    Answers:

    • 18m/s

    • 24 m/s

    • 12 m/s

    • 36 m/s

  • 20.

    What is the relationship between flow speed at point 2 and point 1 if a pipe with flowing water has a cross-sectional area five times greater at point 2 than at point 1?

    Answers:

    • {eq}v_{1}=5v_{2} {/eq}

    • {eq}v_{2}=5v_{1} {/eq}

    • {eq}v_{1}=25v_{2} {/eq}

    • {eq}v_{2}=25v_{1} {/eq}

  • 21.

    The blood flowing in the artery has a velocity {eq}v {/eq}. Due to some diseases, the area of the artery reduces to 0.8 times the initial area. Calculate the speed of the blood in the contracted part of the artery.

    Answers:

    • 1.25{eq}v {/eq}

    • 0.75{eq}v {/eq}

    • 0.8{eq}v {/eq}

    • 1.5{eq}v {/eq}

  • 22.

    An engineer is tasked to increase the fluid's velocity at the exit of a pipeline. The area at the inlet of the pipe is {eq}50\ \rm cm^{2} {/eq} and the velocity of the fluid is 50 cm/s. The engineer has decided to decrease the area of the pipe at the exit. Calculate the velocity at the exit of the pipe, if the area is reduced to {eq}40\ \rm cm^{2} {/eq}

    Answers:

    • 62.5 cm/s

    • 70.0 cm/s

    • 67.5 cm/s

    • 60.0 cm/s

  • 23.

    In the bathroom, the velocity of the water flowing through a 5 cm diameter pipe is 15 cm/s. If a hose of 2.5 cm diameter is attached to the pipe, calculate the velocity of water flowing through the hose.

    Answers:

    • 45 cm/s

    • 30 cm/s

    • 60 cm/s

    • 15 cm/s

  • 24.

    If the radius of a pipe is increasing, the velocity of the fluid flowing through the pipe will?

    Answers:

    • First decrease then increase

    • Decrease

    • Do not change

    • Increase

  • 25.

    An incompressible fluid is flowing through a pipe having a radius of 60 cm with a velocity of 50 cm/s. If the radius of the pipe at the exit is 40 cm, calculate the velocity of the fluid at the exit of the pipe.

    Answers:

    • 112.5 cm/s

    • 11.25 cm/s

    • 75 cm/s

    • 750 cm/s

  • 26.

    Air enters a nozzle having an inlet diameter of 12.5 cm with a velocity of 100 cm/s. Calculate the velocity of air at the exit where the diameter is 10 cm.

    Answers:

    • 156.25 cm/s

    • 135.00 cm/s

    • 125.00 cm/s

    • 166.25 cm/s

  • 27.

    Air enters a diffuser through an inlet with a diameter of 10 cm. The air's velocity upon entering is 80 cm/s. Calculate the velocity of air at the exit point where the diameter is 15 cm.

    Answers:

    • 2.556 cm/s

    • 25.56 cm/s_

    • 35.56 cm/s

    • 3.556 cm/s

  • 28.

    The radius at the inlet of the pipe is {eq}5\ \rm m {/eq} and the radius at the exit of the pipe is 7.5 m. If the velocity of the liquid at the exit of the pipe is 100 m/s, what is the velocity of liquid while entering the pipe?

    Answers:

    • 2.25 m/s

    • 22.5 m/s

    • 225 m/s

    • 0.225 m/s

  • 29.

    A nozzle is attached to a pipe. The inlet area of the nozzle is {eq}7.5\ \rm cm^{2} {/eq} and the velocity of water entering the nozzle is {eq}25\ \rm m/s {/eq}. If the outlet area of the nozzle is {eq}15\ \rm cm^{2} {/eq}, the velocity of water at the exit of the nozzle is?

    Answers:

    • 12.5 cm/s

    • 12.5 m/s

    • 25 cm/s

    • 25 m/s

  • 30.

    The velocity of air entering a 12.5 cm diameter diffuser is 50 m/s. If the diameter at the exit of the diffuser is 20 cm, find the velocity of the air as it leaves the diffuser.

    Answers:

    • 15.53 m/s

    • 18.53 m/s

    • 17.53 m/s

    • 19.53 m/s

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