Worksheet: Conservation of Energy in Moving Fluids

In this worksheet, we will practice using the Bernoulli equation to describe the relation of the pressure exerted by a fluid flow to its total energy.

Q1:

The Bernoulli equation applies to the streamlines of smoothly flowing fluids of constant density. The equation can be written in the form 𝑝 + 𝜌 𝑔 + 1 2 𝜌 𝑣 = 𝑘 , where 𝑘 is a constant. In the equation, 𝑝 is term (i), 𝜌 𝑔 is term (ii), and 1 2 𝜌 𝑣 is term (iii).

Which term represents the dynamic pressure exerted by a fluid?

  • ATerm (iii)
  • BTerm (ii)
  • CNone of the terms
  • DTerm (i)

Which term represents the hydrostatic pressure exerted by a fluid?

  • ANone of the terms
  • BTerm (iii)
  • CTerm (ii)
  • DTerm (i)

Which term represents the static pressure exerted by a fluid?

  • ATerm (ii)
  • BTerm (iii)
  • CNone of the terms
  • DTerm (i)

Q2:

Water with a constant density of 1,000 kg/m3 flows smoothly along a streamline. The water enters the streamline moving at 3.33 m/s and exits the streamline moving at 2.72 m/s. The vertical displacement of the exit point of the streamline from the entry point of the streamline is 0.164 m.

What is the change in the static pressure exerted by the fluid between the entry and exit points of the streamline?

Does the static pressure exerted by the fluid increase or decrease along the streamline?

  • AIt decreases.
  • BIt increases.

Q3:

The Bernoulli equation applies to the streamlines of smoothly flowing fluids of constant density. The equation relates the density of the fluid, 𝜌 ; the static pressure exerted by the fluid, 𝑝 ; the velocity of the fluid, 𝑣 ; the acceleration due to gravity, 𝑔 ; and the vertical displacement of the fluid, . The equation can be written in the form 𝑝 + 𝜌 𝑔 + 1 2 𝜌 𝑣 = 𝑘 , where 𝑘 is a constant.

The term 1 2 𝜌 𝑣 in the equation represents the energy per unit of the fluid along the streamline.

  • Akinetic, volume
  • Bkinetic, length
  • Ckinetic, mass
  • Dmechanical, time
  • Emechanical, length

The term 𝜌 𝑔 in the equation represents the energy per unit of the fluid along the streamline.

  • Akinetic, length
  • Bkinetic, time
  • Cmechanical, mass
  • Dgravitational potential, mass
  • Egravitational potential, volume

Q4:

Water with a constant density of 1,000 kg/m3 flows smoothly along a streamline 𝑆 , as shown in the diagram. The water passes through a pipe that narrows along its length, entering the pipe at 5.5 m/s. The center of the wider end of the pipe is 2.2 m below the center of the narrower end of the pipe. The static pressure exerted by the water where it leaves the pipe equals the static pressure exerted by the water where it enters the pipe. At what speed does the water exit the pipe?

Q5:

Water with a constant density of 1,000 kg/m3 flows smoothly along a streamline 𝑆 , as shown in the diagram. The water passes through a pipe that widens along its length. The center of the wider end of the pipe is 1.4 m below the center of the narrower end of the pipe. Water enters and exits the pipe at the same speed. How much greater is the static pressure exerted by the water where the water leaves the pipe than the static pressure exerted by the water where the water enters the pipe? Answer to two significant figures.

Q6:

Water with a constant density of 1,000 kg/m3 flows smoothly along a streamline 𝑆 , as shown in the diagram. The streamline 𝑆 passes at constant height along a wedge-shaped channel that has a cross-sectional area of 0.75 m2 where the water enters the channel and a cross-sectional area of 0.45 m2 where the water exits the channel. The water enters the channel moving at 1.5 m/s. How much greater is the static pressure exerted by the water where it enters the channel than where it leaves it?

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