Determine the bulk modulus of elasticity of a liquid, if the pressure is increased from 7N/m^2 to 13N/m^2. The volume of the liquid decrease by 0.15%
To determine the bulk modulus of elasticity of a liquid, we can use the formula:
Bulk modulus (K) = (change in pressure) / ((change in volume / original volume) * pressure)
Given:
Initial pressure (P₁) = 7 N/m²
Final pressure (P₂) = 13 N/m²
Change in pressure (ΔP) = P₂ - P₁ = 13 N/m² - 7 N/m² = 6 N/m²
Change in volume (ΔV) = -0.15% (or -0.0015) of the original volume
Original volume (V) = 1 (since it is a ratio)
Substituting the values into the formula:
Bulk modulus (K) = (6 N/m²) / ((-0.0015) * 1 * 7 N/m²)
Bulk modulus (K) = 6 N/m² / (-0.0105 N/m²)
Bulk modulus (K) ≈ -571.43 N/m²
Therefore, the bulk modulus of elasticity for the given liquid is approximately -571.43 N/m². Note that the negative sign indicates that the liquid is compressible.
To determine the bulk modulus of elasticity (K) of a liquid, we can use the formula:
K = -VΔP / ΔV
Where:
K is the bulk modulus of elasticity
V is the initial volume of the liquid
ΔP is the change in pressure
ΔV is the change in volume
Given:
Initial pressure, P1 = 7 N/m^2
Final pressure, P2 = 13 N/m^2
Change in pressure, ΔP = P2 - P1 = 13 N/m^2 - 7 N/m^2 = 6 N/m^2
The volume change can be calculated using the percentage change formula:
Percentage change = (final value - initial value) / initial value * 100
So, -0.15% = (ΔV / V) * 100, since the volume decrease is given as -0.15%
Rearranging the equation, we have:
ΔV / V = -0.15% / 100 = -0.0015
Now, substituting the known values into the bulk modulus formula:
K = -VΔP / ΔV
K = -V * (P2 - P1) / (ΔV / V)
K = -V * (6 N/m^2) / (-0.0015)
Since we don't have specific values of the initial volume (V), we can't calculate the exact value of K. However, by plugging in the value of V, you can solve for K using the given formula.
4000 N/meter squer
well, you have
K = -∆p/(∆V/Vo)
plug in your numbers, right?