Topic: Fluid Mechanics
For flow through a horizontal pipe, the pressure gradient $\frac{dp}{dx}$ in the flow direction is-
- A. +ve
- B. 1
- C. Zero
- D. -ve
Answer: D. -ve
Explanation: According to Bernoulli's equation with head loss, $\frac{p_{1}}{\rho g} + \frac{v_{1}^{2}}{2g} + z_{1} = \frac{p_{2}}{\rho g} + \frac{v_{2}^{2}}{2g} + z_{2} + h_{f}$. For horizontal uniform pipe, $v_{1}=v_{2}$ and $z_{1}=z_{2}$, so $\frac{p_{1}-p_{2}}{\rho g} = h_{f}$, meaning $p_{1} > p_{2}$. Pressure decreases in the direction of flow, hence the pressure gradient $\frac{dp}{dx}$ is negative.