Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At point 1 the cross-sectional area of the pipe is 0.070 m2, and the magnitude of the fluid velocity is 3.50 m/s. (c) Calculate the volume of water discharged from the open end of the pipe in 1.00 hour.

Ch 12: Fluid Mechanics

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

All textbooks

Young & Freedman Calc 15th Edition

Ch 12: Fluid Mechanics

Problem 40c

Chapter 12, Problem 40c

Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At point 1 the cross-sectional area of the pipe is 0.070 m², and the magnitude of the fluid velocity is 3.50 m/s. (c) Calculate the volume of water discharged from the open end of the pipe in 1.00 hour.

Verified step by step guidance

First, understand that the problem involves fluid flow through a pipe with varying cross-sectional areas. We need to calculate the volume of water discharged from the pipe over a given time period.

Use the principle of continuity for incompressible fluids, which states that the product of cross-sectional area (A) and fluid velocity (v) is constant along the pipe: A1 * v1 = A2 * v2. However, since we are calculating the discharge volume, we focus on the flow rate at point 1.

Calculate the flow rate at point 1 using the formula: Flow rate = A1 * v1. Substitute the given values: A1 = 0.070 m^2 and v1 = 3.50 m/s.

Determine the total volume of water discharged over 1 hour. Use the formula: Volume = Flow rate * time. Convert 1 hour into seconds (1 hour = 3600 seconds) to ensure consistent units.

Substitute the calculated flow rate and the time in seconds into the volume formula to find the total volume of water discharged from the pipe.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Continuity Equation

The continuity equation in fluid dynamics states that the mass flow rate of a fluid must remain constant from one cross-section of a pipe to another, assuming incompressible flow. It is expressed as A1V1 = A2V2, where A is the cross-sectional area and V is the fluid velocity. This principle helps determine how changes in pipe diameter affect fluid velocity.

Volume Flow Rate

Volume flow rate is the volume of fluid that passes through a given surface per unit time, typically measured in cubic meters per second (m³/s). It is calculated as the product of the cross-sectional area of the pipe and the fluid velocity (Q = A × V). This concept is crucial for determining the total volume of fluid discharged over a specific period.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this context, converting the time from hours to seconds is necessary to ensure consistency in units when calculating the volume of water discharged. This involves multiplying the time in hours by 3600 to convert it to seconds.

Recommended video:

Guided course

07:46

Unit Conversions

Related Practice

Textbook Question

A small circular hole 6.00 mm in diameter is cut in the side of a large water tank, 14.0 m below the water level in the tank. The top of the tank is open to the air. Find (a) the speed of efflux of the water and (b) the volume discharged per second.

views

Textbook Question

A shower head has 20 circular openings, each with radius 1.0 mm. The shower head is connected to a pipe with radius 0.80 cm. If the speed of water in the pipe is 3.0 m/s, what is its speed as it exits the shower-head openings?

views

Textbook Question

A soft drink (mostly water) flows in a pipe at a beverage plant with a mass flow rate that would fill 220 0.355-L cans per minute. At point 2 in the pipe, the gauge pressure is 152 kPa and the cross-sectional area is 8.00 cm². At point 1, 1.35 m above point 2, the cross-sectional area is 2.00 cm². Find the (b) volume flow rate. (c) flow speeds at points 1 and 2.

views

Textbook Question

A cubical block of wood, 10.0 cm on a side, floats at the interface between oil and water with its lower surface 1.50 cm below the interface (Fig. E12.33). The density of the oil is 790 kg/m³. (a) What is the gauge pressure at the upper face of the block? (b) What is the gauge pressure at the lower face of the block?

BIO. Artery Blockage. A medical technician is trying to determine what percentage of a patient's artery is blocked by plaque. To do this, she measures the blood pressure just before the region of blockage and finds that it is 1.20×10⁴ Pa, while in the region of blockage it is 1.15×10⁴ Pa. Furthermore, she knows that blood flowing through the normal artery just before the point of blockage is traveling at 30.0 cm/s, and the specific gravity of this patient's blood is 1.06. What percentage of the cross-sectional area of the patient's artery is blocked by the plaque?