上游充通大睾 4.4 Pressure Variation with Depth Shanghai Jiao Tong University Consider a small vertical cylinder of fluid in equilibrium,where positive is pointing vertically upward.Suppose the origin Z-0 is set at the free surface of the fluid.Then the pressure variation at a depth=-h below the free surface is governed by (p+△p)A+W=pA → △pA+PgA△z=0 0 → △p=-P8△2 h → dp P+Ap dz -P8 cross sectional area=A or dp dz =一Y (as△z→0) p Therefore,the hydrostatic pressure increases linearly with depth at the rate of the specific weight y=pg of the fluid.Shanghai Jiao Tong University 4.4 Pressure Variation with Depth Consider a small vertical cylinder of fluid in equilibrium, where positive z is pointing vertically upward. Suppose the origin z = 0 is set at the free surface of the fluid. Then the pressure variation at a depth z = -h below the free surface is governed by ( ) 0 or (as 0) p p A W pA pA gA z p gz dp g dz dp z dz ρ ρ ρ γ +Δ + = ⇒ Δ + Δ= ⇒ Δ =− Δ ⇒ =− =− Δ → Δz p p+Δp W cross sectional area = A 0 h Therefore, the hydrostatic pressure increases linearly with depth at the rate of the specific weight γ ≡ ρ g of the fluid