Question

For a compressible fluid, sonic velocity is

• A. a property of the fluid
• B. always given by $(\gamma RT{)}^{1/2}$ where $\gamma ,R$ and T are respectively the ratio of specific heats, gas constant and temperature in K
• C. always given by ${\left(\frac{\partial p}{\partial \rho }\right)}_s^{1/2},wherep,\rho ands$ are respectively pressure , density ans entropy
• D. always greater then the veocity of fluid at any location.

Answer 1

The correct option is C always given by ${\left(\frac{\partial p}{\partial \rho }\right)}_s^{1/2},wherep,\rho ands$ are respectively pressure , density ans entropy

Sonic velocity or velocity of sound:
(i) The velocity of sound depends upon the temperature and nature of steam.
(ii) In case of compressible fluid, sonic velocity.
$C=\sqrt{\frac{dp}{d\rho }}$
(iii) In case of Ideal gas, sonic velocity
$C=\sqrt{\gamma RT}$