Explanation Given: The bulk modulus ( E V ) is 2.20 GPa . The depth of the water is 300 m . Density of the water ( ρ ) is 1000 kg/m 3 Calculation: Calculate the bulk modulus for incompressible fluid. E V = d p d V / V (I) Here, the pressure at depth 300 m is p and Volume is V . Calculate the density of water ( ρ ) using the formula. V = m ρ Here, the mass is m . Find the d V V parameter. d V V = − m / ρ 2 d ρ m / ρ = − d ρ ρ Substitute ( − d ρ ρ ) in Equation (1). E V = − d p ( d ρ / ρ ) Assume that density ( ρ ) as 1 , 000 kg / m 3 and pressure ( p ) as 0 at water surface. Calculate the pressure from 0 to p ; when density changes from 1 , 000 kg / m 3 as depth increases. E V ∫ ρ 0 ρ d ρ ρ = ∫ p 0 p d p Here, the pressure at the surface (absolute pressure) is p 0 and the density at the surface is ρ 0 . Substitute p 0 = 0 , ρ 0 = 1 , 000 kg / m 3 , and E V = 2.20 G P a in the above equation. ( 2.20 × 10 9 N / m 2 ) ∫ 1 , 000 ρ d ρ ρ = ∫ 0 p d p ( 2.20 × 10 9 ) ln ( ρ 1 , 000 ) = p ρ = 1 , 000 e p ( 2.20 × 10 9 ) (II) Calculate the unit weight of water ( γ ) using the relation. γ = ρ g Here, the acceleration due to gravity is g . Write the expression for The pressure ( p ). p = p 0 + γ z Here, the absolute pressure is p 0 , the unit weight of fluid is γ , and the vertical height is z . Substitute γ = ρ g in the above equation. p = p 0 + ( ρ g ) z Differentiate on both sides of the above equation. d p = ( ρ g ) d z d p ρ = g × d z Substitute Equation (II) for ρ and g = 9

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 2, Problem 17P

To determine

The value of pressure at a depth of 300 m when water is compressible and the value of pressure at a depth of 300 m when water is incompressible.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 16P

Chapter 2, Problem 18P

Students have asked these similar questions

PUNTO 4. calculate their DoF using Gruebler's formula. PUNTO 5. Ground

PUNTO 2. PUNTO 3. calculate their DoF using Gruebler's formula. III IA

calculate their DoF using Gruebler's formula. PUNTO 6. PUNTO 7. (Ctrl)

Chapter 2 Solutions

Fluid Mechanics (2nd Edition)

Ch. 2 - Prob. 1FP Ch. 2 - The container is partially filled with oil, water,...Ch. 2 - The U-tube manometer is filled with mercury,...Ch. 2 - The tube is filled with mercury from A to B, and...Ch. 2 - The air pressure in the pipe at A is 300 kPa....Ch. 2 - Determine the absolute pressure of the water in...Ch. 2 - The bin is 1.5 m wide and is filled with water to...Ch. 2 - The bin is 2 m wide and is filled with oil to the...Ch. 2 - The 2-m-wide container is filled with water to the...Ch. 2 - Determine the resultant force of the water acting...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.