Skip to main content
Ch 14: Fluids and Elasticity
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 14: Fluids and ElasticityProblema 63b
Capitolo 14, Problema 63b

Air flows through the tube shown in FIGURE P14.63. Assume that air is an ideal fluid. What is the volume flow rate?

Guida verificata passo dopo passo
1
Step 1: Identify the given data from the problem and the diagram. The air density is \( \rho_{\text{air}} = 1.28 \; \text{kg/m}^3 \), the mercury density is \( \rho_{\text{Hg}} = 13600 \; \text{kg/m}^3 \), the diameter of the wide section of the tube is \( D_1 = 3.0 \; \text{cm} \), and the diameter of the narrow section is \( D_2 = 3.0 \; \text{mm} \). The height difference in the mercury column is \( h = 4.5 \; \text{cm} \).
Step 2: Use Bernoulli's equation to relate the pressures and velocities in the wide and narrow sections of the tube. Bernoulli's equation is \( P_1 + \frac{1}{2} \rho_{\text{air}} v_1^2 = P_2 + \frac{1}{2} \rho_{\text{air}} v_2^2 \), where \( P_1 \) and \( P_2 \) are the pressures, and \( v_1 \) and \( v_2 \) are the velocities in the wide and narrow sections, respectively.
Step 3: Relate the pressure difference \( P_1 - P_2 \) to the height difference in the mercury column using the hydrostatic pressure formula: \( P_1 - P_2 = \rho_{\text{Hg}} g h \), where \( g \) is the acceleration due to gravity (\( 9.8 \; \text{m/s}^2 \)).
Step 4: Use the continuity equation to relate the velocities in the wide and narrow sections: \( A_1 v_1 = A_2 v_2 \), where \( A_1 = \pi (D_1/2)^2 \) and \( A_2 = \pi (D_2/2)^2 \) are the cross-sectional areas of the wide and narrow sections, respectively.
Step 5: Combine the equations from Steps 2, 3, and 4 to solve for the volume flow rate \( Q \), which is given by \( Q = A_1 v_1 = A_2 v_2 \). Substitute the known values and solve for \( Q \).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
18m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Ideal Fluid

An ideal fluid is a theoretical fluid that is incompressible and has no viscosity. This means it flows without any internal friction and does not change its density regardless of pressure changes. In the context of this problem, assuming air as an ideal fluid simplifies calculations related to flow rates and pressure changes, allowing the application of Bernoulli's principle.
Video consigliato:
Percorso guidato
03:41
Ideal vs Real Fluids

Bernoulli's Principle

Bernoulli's principle states that in a flowing fluid, an increase in the fluid's speed occurs simultaneously with a decrease in pressure or potential energy. This principle is crucial for understanding how the velocity of air changes as it moves through the tube, particularly in areas where the cross-sectional area varies, affecting the flow rate and pressure distribution.
Video consigliato:
Percorso guidato
14:47
Diffraction with Huygen's Principle

Volume Flow Rate

Volume flow rate is a measure of the volume of fluid that passes through a given surface per unit time, typically expressed in cubic meters per second (m³/s). It is calculated by multiplying the cross-sectional area of the flow by the fluid's velocity. In this problem, determining the volume flow rate involves using the dimensions of the tube and the velocity of the air to find how much air flows through the tube over time.
Video consigliato:
Percorso guidato
6:34
Fluid Speed & Volume Flow Rate
Pratica correlata
Domanda del libro di testo

Water from a vertical pipe emerges as a 10-cm-diameter cylinder and falls straight down 7.5 m into a bucket. The water exits the pipe with a speed of 2.0 m/s. What is the diameter of the column of water as it hits the bucket?

2002
views
Domanda del libro di testo

Air flows through the tube shown in FIGURE P14.62 at a rate of 1200 cm³/s. Assume that air is an ideal fluid. What is the height h of mercury in the right side of the U-tube?

2523
views
1
rank
Domanda del libro di testo

A water tank of height h has a small hole at height y. The water is replenished to keep h from changing. The water squirting from the hole has range 𝓍. The range approaches zero as y → 0 because the water squirts right onto the ground. The range also approaches zero as y → h because the horizontal velocity becomes zero. Thus there must be some height y between 0 and h for which the range is a maximum. Find an algebraic expression for the flow speed v with which the water exits the hole at height y.

2324
views
Domanda del libro di testo

20°C water flows through a 2.0-m-long, 6.0-mm-diameter pipe. What is the maximum flow rate in L/min for which the flow is laminar?

1689
views
Domanda del libro di testo

A cylindrical tank of radius 𝑅, filled to the top with a liquid, has a small hole in the side, of radius 𝓇, at distance d below the surface. Find an expression for the volume flow rate through the hole.

2771
views
Domanda del libro di testo

A hurricane wind blows across a 6.0 m x 15.0 m flat roof at a speed of 130 km/h. What is the pressure difference?

2214
views
1
rank