Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 3, Problem 35P

a)

To determine

The power required for the car to climb the uphill road at the constant velocity.

a)

Expert Solution
Check Mark

Explanation of Solution

Given:

Mass of the car (m) is 1150kg.

Height climbed by the car in the uphill road (h) is 100m.

Slope of the road (θ) is 30°.

Time interval (Δt) is 12s.

Acceleration due to gravity (g) is 9.81m/s2.

Calculation:

Calculate the vertical rise of the car (Δz).

  Δz=hsinθ=(100m)(sin30°)=50m

The change in kinetic energy of the car is zero because the velocity of the car is constant.

  W˙a=0kW

Calculate the change in potential energy of the car (W˙g).

  W˙g=mgΔzΔt=(1150kg)(9.81m/s2)(50m12s)=(1150kg)(9.81m/s2)(50m12s)(1kJ1000kgm2/s2)=47kW

Calculate the power required for the car to climb the uphill road at the constant velocity (W˙total).

  W˙total=W˙a+W˙g=0kW+47kW=47kW

Thus, the power required for the car to climb the uphill road at the constant velocity is 47kW_.

b)

To determine

The power required for the car to climb the uphill road from rest to the final velocity.

b)

Expert Solution
Check Mark

Explanation of Solution

Given:

Initial velocity of the car (V1) is 0m/s.

Final velocity of the car (V2) is 30m/s.

Calculation:

Calculate the change in kinetic energy of the car (W˙a).

  W˙a=12m(V22V12)Δt=12(1150kg)[(30m/s)2(0m/s)2]12s=12(1150kg)[(30m/s)2(0m/s)2]12s(1kJ1000kgm2/s2)=43.1kW

Calculate the power required for the car to climb the uphill road rest to the final velocity (W˙total).

  W˙total=W˙a+W˙g=43.1kW+47kW=90.1kW

Thus, the power required for the car to climb the uphill road from rest to the final velocity is 90.1kW_.

c)

To determine

The power required for the car to climb the uphill road from initial velocity to the final velocity.

c)

Expert Solution
Check Mark

Explanation of Solution

Given:

Initial velocity of the car (V1) is 35m/s.

Final velocity of the car (V2) is 5m/s.

Calculation:

Calculate the change in kinetic energy of the car (W˙a).

  W˙a=12m(V22V12)Δt=12(1150kg)[(5m/s)2(35m/s)2]12s=12(1150kg)[(5m/s)2(35m/s)2]12s(1kJ1000kgm2/s2)=57.5kW

Calculate the power required for the car to climb the uphill road from initial velocity to the final velocity (W˙total).

  W˙total=W˙a+W˙g=57.5kW+47kW=10.5kW

Thus, the power required for the car to climb the uphill road from initial velocity to the final velocity is 10.5kW_.

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Chapter 3 Solutions

Fundamentals of Thermal-Fluid Sciences

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