Q: If the height $$h of $$mercury in the U-tube in FIGURE P14.62 is measured to be 1.2 cm, what is the pressure difference between the two sides of the tube? (Density of mercury $$\rho_{Hg} = 13,600 kg/m$^3$$, $$g = 9.8 m/s$^2)$$

The pressure difference is $$\Delta P = \rho_{Hg} g h = 13,600 \times 9.8 \times 0.012 = 1,598 Pa$$

Q: If the density of air is $$1.2 kg/m$^3$$, and the speed in the narrow section is $$v_2$$, what is the pressure difference between the wide and narrow sections according to Bernoulli’s equation?

$$\Delta P = \frac{1}{2} \times 1.2 \times (v_2$^2 - v_1$^2)$$

Question 1

In FIGURE P14.62, air flows through a tube at a rate of 1200 cm$$^3/s. If $$the diameter of the exit tube is 4.0 mm and the diameter of the wider section is 2.0 cm, what is the speed of air in the wider section? (Assume air is incompressible and ideal.)

Accepted Answer

Question 2

Using Bernoulli’s equation, which expression correctly relates the pressure difference between the wide and narrow sections of the tube in FIGURE P14.62, given the air speeds $$v_1$$ and $$v_2$$?

Accepted Answer

$$P_1$$ - $$P_2$$ = \frac{1}{2} \rho ($$v_2^2$$ - $$v_1^2$$)$$

Question 3

If the height $$h of $$mercury in the U-tube in FIGURE P14.62 is measured to be 1.2 cm, what is the pressure difference between the two sides of the tube? (Density of mercury $$\rho_{Hg} = 13,600 kg/m$^3$$, $$g = 9.8 m/s$^2)$$

Accepted Answer

The pressure difference is $$\Delta P = ho_{Hg} g h = 13,600 	imes 9.8 	imes 0.012 = 1,598 Pa$$

Question 4

Given the flow rate of 1200 cm$$^3/s $$and the exit diameter of 4.0 mm in FIGURE P14.62, what is the speed of air at the exit?

Accepted Answer

Question 5

If the air is assumed to be an ideal fluid, which principle allows us to relate the pressure difference to the height of mercury in the U-tube?

Accepted Answer

Bernoulli’s principle

Question 6

In FIGURE P14.62, if the pressure in the wide section is higher than in the narrow section, what happens to the height $$h of $$mercury in the U-tube?

Accepted Answer

The height $$h$$ increases

Question 7

Which equation best describes the conservation of mass for the air flow in FIGURE P14.62?

Accepted Answer

$$A_1$$ $$v_1$$ = $$A_2$$ $$v_2$$

Question 8

If the air flow rate is doubled in FIGURE P14.62, what happens to the height $$h of $$mercury in the U-tube?

Accepted Answer

The height $$h$$ increases

Question 9

If the density of air is $$1.2 kg/m$^3$$, and the speed in the narrow section is $$v_2$$, what is the pressure difference between the wide and narrow sections according to Bernoulli’s equation?

Accepted Answer

$$\Delta P = \frac{1}{2} 	imes 1.2 	imes (v_2$^2 - v_1$^2)$$

Question 10

A student claims that increasing the diameter of the exit tube in FIGURE P14.62 will increase the height $$h of $$mercury in the U-tube. Is this correct?

Accepted Answer

No, increasing the diameter decreases the velocity and thus decreases $$h$$

Question 11

If the U-tube contains water instead of mercury, how would the height $$h$$ change for the same pressure difference?

Accepted Answer

The height $$h$$ would increase

Question 12

Which of the following best explains why the pressure is lower in the narrow section of the tube in FIGURE P14.62?

Accepted Answer

The velocity of air is higher in the narrow section, leading to lower pressure according to Bernoulli’s principle

Question 13

If the atmospheric pressure is 101,325 Pa, what is the absolute pressure in the wide section of the tube if the height $$h of $$mercury is 1.2 cm?

Accepted Answer

The absolute pressure is $$P = 101,325 + 1,598 = 102,923 Pa$$

Question 14

Which real-world device uses the principle demonstrated in FIGURE P14.62 to measure fluid flow?

Accepted Answer

A Venturi meter

Question 15

If the flow rate in FIGURE P14.62 is kept constant but the fluid is changed from air to water, what happens to the height $$h of $$mercury in the U-tube?

Accepted Answer

The height $$h$$ decreases

Question 16

If the U-tube in FIGURE P14.62 is open to the atmosphere on both sides, what does the height $$h of $$mercury represent?

Accepted Answer

The height $$h$$ represents the pressure difference between the two sections of the tube

Applying Bernoulli’s Principle and Fluid Dynamics to a U-Tube Manometer

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